What happens when custard ingredients are reordered?

Question

In the mathematics book How to Bake Pi by Eugenia Cheng in the chapter titled Sameness she mentions the making of custard. She explains that although custard has only three ingredients the order of how they are mixed together is important. In a more mathematical notation:

custard = (egg yolks + sugar) + milk doesn't equal egg yolks + (sugar + milk) = not custard.

So my question: What happens if we mix the sugar and milk first before whisking in the egg yolks, what is the result; and why do we not get custard?

Addendum: I appreciate I could simply try this experimentally, but I would prefer not to waste food unless I can then do something with the resulting mixture. If there is something I can do with the result, let me know too!

Answer 1

By and large, the statement in the book is wrong. You can certainly make custard with the second way of mixing.

I said "by and large", because the order is not completely arbitrary. It will be easier to make custard if you add sugar to the eggs first. This is because eggs are very prone to curdling when heated, and an egg+sugar mixture happens to be less curdle-prone. But this doesn't mean that the second method is wrong, it just requires more precise work in order to not fail. If you execute them properly, both methods will give you actual custard.

So the statement combination

custard = (egg yolks + sugar) + milk

egg yolks + (sugar + milk) = not custard.

is incorrect. The correct statements would be

(egg yolks + sugar) + milk = (custard OR curdled mass)

egg yolks + (sugar + milk) = (custard OR curdled mass).

Which result you get depends in both cases on the cook's skill and on a few external factors like precise temperature control. The contribution of the mixing order exists, but is relatively minor.

Without having read the book, I can only take a shot at the author's point from your description. Still, I think I get what she was trying to illustrate - not every way of mixing ingredients will give you the same dish. For example, in Ruhlman's classification of cake layer types, pound cake and sponge cake are made from the exact same ingredients in the exact same ratio, but with different mixing processes. Or you can stretch it further and note that making a crepe and filling it with Mornay sauce is not the same dish as mixing all ingredients in a blender from the start and baking cheesy pancakes.

If you want to experiment, just do it. Even if you fail, the result is perfectly edible. It just doesn't meet the expectations of people who want to eat professionally-made custard. (I say professionally made, because I know some families where the custard always gets overcooked, and they see it as normal and enjoy the dish fully).