egg-whiteseggs
I have seen different recipes for Crème anglaise. Some use only yolks, others uses whole eggs with white.
I usually like this "eggy" taste which may comes from the egg whites, but I would like to know which should be the proper way to make crème anglaise.
Egg yolks and egg whites have very different roles in baking. You can almost never replace them. And in the cases in which you can, you will end up with a different texture.
In this case, it won't be sure disaster to replace, but I would be very reluctant to do it. Flourless recipes are finicky. Flour holds stuff together. Nut flours don't hold anything together, they need a binding agent. Egg whites are a good binding agent. Egg yolks are not only not good as a binding agent (except in certain circumstances, for example in custards - but you don't have this here), they are even a lubricant and as such will interfere with the binding done by the egg whites.
If you substitute here, you will not only change the taste, you risk your cookies crumbling apart in your hands.
In general, don't replace stuff in baking recipes. They are hard to design right. Even if you have some issues (e.g. allergies), it is easier to find an existing recipe without the offending ingredient than to try to tweak an existing one to work with different ingredients. Eggs are especially hard to substitute. Such a reason like "not wanting to waste" loses its sense if what you end up with is bad cookies, which are a much worse waste of products. And besides, you can do many more interesting things with a yolk than just scrambled eggs. In fact, I am frequently throwing out whites because I have found no use for them after doing something with the yolks.
If you still want to go ahead and try if the cookies work for you, try using 3 whole eggs. 2 eggs are nowhere near enough to substitute for 4 egg whites. Not only are the yolks smaller than the whites volume-wise, they will also not deliver you the binding proteins you need so badly.
Milk and cream are essentially made up of water, fat, and protein molecules. Within milk and cream, the fat globules are already emulsified in the surrounding water by casein (one of the proteins found in milk and cream). This means that casein molecules surround each fat globule and prevent them from coming together. This is why milk doesn't separate into fat and water, even though it's made up of two substances that don't naturally mix.
However, casein is a little too good at emulsifying the fat. When we add egg yolks, the lecithin in the yolk displaces some of the casein surrounding each fat globule. This partially destabilizes the emulsion of the milkfat by casein and allows some of the fat globules to partially coalesce when the ice cream base is chilled and aged overnight.
Partially coalesced fat forms a network that traps and stabilizes the air that is incorporated into ice cream while churning, leading to slower melting, better shape retention, and overall improved texture. Lecithin is why we need egg yolks.
Egg whites, however, are mostly water and don't contain lecithin. Adding water to your ice cream base leads to an unfavorable icy texture in the final product and doesn't contribute to partial coalescence of fat. Water is why egg whites are typically left out.
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Best Answer
The proper way (French Larousse Culinaire reference) is to use only egg yolks.
But like everything else in cuisine recipes, whatever you like is good enough.