When we were young my poor mother used to have to make two different thicknesses of custard to please her fussy children. Of course, now we know - having been mothers ourselves and done our own bit of pandering to our own children - really she should not have given us the option. But she did. She was a loving mum. I can't remember now who liked it thick and who liked it thin, but I do know there was a definite preference. Maybe not as thick as the one on the left, and probably thinner than the one on the right, but different enough to have to make two separate batches. And I fear it was not properly made custard either, but made with Bird's custard powder. I guess the difference would have been the proportion of liquid to powder.
Custard, in fact, is one of those sauces that has a range of uses and so can quite rationally be made in consistencies to pretty solid - for various dessert puddings and tarts, what is crème caramel but a set custard after all, and to pretty runny as a sauce over something else. These days I think I'm probably a bit of a middle way kind of person.
There are various ways to thicken a sauce - or anything else for that matter. The most obvious ones are flour, eggs and boiling it all away.
Thickening a sauce with flour is something I didn't really learn until I started following recipes and my initial experiments were somewhat variable. They often turned out lumpy until a friend cheerfully said, that if that happened all you had to do was pour it through a sieve and push out the lumps. It works every time let me tell you. If you're a real stickler for doing things properly then I guess you should do it in a double boiler - a dish or a pan balanced over boiling water, or at least a very low heat. But I have to confess that these days I just wing it on a pretty low heat. melt your butter (or heat your oil), add your flour stir until smooth and the rawness has gone away then add your liquid slowly, whisking all the time. Keep whisking whilst it thickens. And this is where I lose patience, because it can take a while, so I probably increase the heat too much. But generally in the end I get there now. Partly because of that sieve trick but also these days you can use an electric beater to beat out the lumps - if you have any. Of course, you really should have warmed your liquid before adding it anyway. The colder the liquid the higher the risk. Another way of adding the flour is to mix the flour with a little of the warm liquid you are using until you have a thin paste, and then add this to your sauce. You could use cornflour too - it doesn't lump like flour, but it always seems somehow artificial to me. Like those artificial gravy mixes that you can get. Just add flour rather than that. And I'm ashamed to say that my mother used to make her gravy with Bisto, and I learnt to do it with just flour from my mother-in-law, who, otherwise was not nearly as good a cook as my mother. It was the times I guess.
Flour will thicken your sauce in other ways too. Beurre manié is a well known technique. Instead of making your flour into a paste with liquid, mash your flour into some butter and then add the resultant paste to the liquid. Or - if you toss your meat, or fish, or veggies in flour before you brown them before adding liquid then the sauce it cooks in will be thicker too as the flour somehow seeps into the sauce. This is why I coat my meatballs in flour before frying them before putting in the tomato sauce. You end up with a deliciously thick sauce. Careful though - there's more danger of everything sticking to the bottom of the pan too. So watch it. But I'm sure you know all of this.
Eggs are even trickier - if you're not careful here you end up with scrambled eggs rather than a proper sauce. Again the mantra is slow and not too hot. But these days with the help of blenders, processors and electric beaters there are lots of ways of making the whole process a lot easier. I even saw somebody suggest making it in a microwave. Go to Delia for a modern way to make Hollandaise sauce or Jamie for a rather more authentic one. Not that Hollandaise is the only egg thickened sauce of course. Eggs can be used to thicken soups and other sauces - in which case you would add some of the liquid slowly to beaten eggs and then add this mixture to your soup or sauce. And then, of course, there is mayonnaise - magic. On the whole though I think eggs are really one of the most difficult ways of thickening things.
Does cheese thicken in the same sort of way?
Of course you could just boil your sauce hard and it will reduce and thicken. Well - personally I think it depends what the basis of your sauce is. If it's tomatoes, or something creamy then it will probably work, but if it's just something liquid - like last night's stock resulting from boiling some silverside with vegetables, I think it will just reduce the quantity. I had hoped, last night, that the dumplings I had put on top (flour again) would somehow thicken the sauce - but no. So boiling away things might make your sauce a bit syrupy but then again maybe not and definitely not thick.. You get a jus rather than a creamy sauce
There are a couple of other thickening things though. The first is something I learnt from Elizabeth David, way back when, when I first made her Potage aux champignons à la bressane. You thicken the soup with bread, which is soaked in some of the stock you are making the soup with first, and then crumbled and mixed with the softened mushrooms before adding the stock. And finally, of course, you purée the soup - back then with my faithful mouli, nowadays with a stick blender. I'm pretty sure there are other dishes that use bread to thicken them up as well although a quick search showed up soup almost exclusively. Maybe some stews. Sometimes you just added breadcrumbs to the softened veggies or meat.
And finally you can just add some puréed potatoes - or any other vegetable. Starchy ones though. These also soak up the liquid. If you have potatoes already in your stew or soup then just mash a couple of them into the mix. Of course if you are making soup, puréeing the soup and then reheating it will also thicken it. Just boil away until you've got the right thickness - or add some more liquid if it's too thick.
Sorry - I know you all know all of this. I guess I'm still reflecting on flour and water and also how I could have improved the thickness of last night's liquid. Still next time you're wondering on how to make something thicker it might have refreshed your memory. And how thick you like your sauces is a matter of taste anyway.