Thank you so much, everyone. This is so helpful. I knew you all would come through, and again, am so grateful for the tremendous resource that FOOD52 has always been, thanks to its many generous contributors. Let me tell you about the project to which this relates. Some background: A few months ago and quite by chance, I used some leftover batter from drbabs' extraordinary Chocolate Fantasy Brownie Bites to make some cookies. The dough had been refrigerated, and seemed fairly stiff, so I just dropped it onto a parchment covered baking sheet and 15 minutes later, had a half dozen amazing cookies that were just a bit too "wet". I wanted to do that again for a dessert for a party, but as noted in my question, wanted to use some extra egg yolks. I didn't remember, when I posted the question, that the recipe calls for three eggs. Anyway, based on your answers, I figured that with the 2 whole eggs, and this particular application, I'd probably be okay. So I proceeded accordingly with one adjustment. You see, a few weeks ago while browsing through my ancient (1943 edition) of "The Joy of Cooking," I stumbled on a note by Mrs. Rombauer, about how she'd been urged to include a recipe for butterscotch cookies, which were all the rage then. While urging readers of "The Joy" just to make her butterscotch bar instead, she wrote (with an evident sigh) that anyone who simply had to bake butterscotch cookies should use the bar recipe, but add 2 tablespoons of flour. So I did that too when adapting the Fantasy Brownie Bite recipe. The result? Utter perfection: a moist, slightly chewy cookie with the deep, rich flavor of a fudgy brownie, in a handy, easily-served form. Everyone loved them. Thanks again! ;o)
Yolks are primarily fats, vitamins, and minerals with some protein, and they make baked goods moist and give a smooth texture. Egg whites are mostly protein, so they help set the structure and dry baked goods out.
Based on this understanding substituting a whole egg with two yolks will give you a very tender and moist cookie with a cake-like structure. Because the cookie loses the proteins in the whites, it will likely be crumbly. The flavor wouldn't be affected very much, though the cookie would taste richer.
Per Cook's Illustrated the whites help the cookie to puff and dry out, and the yolks add richness. I think you could still make the cookies, just expect a different texture to the final product than you're used to. Other ideas: you could make French toast with yolks only, citrus curd of one sort or another (I have a mango-lime version posted in my Exotic Pavlova Parfait which you could do a half batch of), you could also add them to scrambled eggs or omelets for an extra delicious version.
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Based on this understanding substituting a whole egg with two yolks will give you a very tender and moist cookie with a cake-like structure. Because the cookie loses the proteins in the whites, it will likely be crumbly. The flavor wouldn't be affected very much, though the cookie would taste richer.