What would happen if I add an extra egg yolk to some cookie dough?

Pecan Sandies are sometimes basically shortbread (flour, butter, sugar, little to no water, no eggs). Other recipes include eggs and baking soda, which will give a softer, more cakelike cookie. If you add an egg yolk to the second type, it probably will make little difference. I'm not sure what the effect will be if you add an egg yolk to the shortbread type. However, I did find a shortbread recipe that includes egg yolks, so I don't think it will be a problem.

I found this article that recommends adding hard-boiled egg yolks to "scones, shortbread, biscuits, cornbread, and cake doughnuts." A shortbread-type Pecan Sandy recipe would fit the bill. Crumble the cooked egg yolk by using a spoon to press it through a sieve.

What happens is this: The tiny bits of cooked yolk intersperse throughout the batter and get in the way of the gluten network that forms when flour mixes with wet ingredients. Gluten is necessary in baked goods to give them structure, but too much makes for a tough, chewy crumb that’s generally undesirable in the pastry world. Cooked egg yolks prevent too much gluten (a.k.a. toughness) from developing without weighing the batter down. The result is a cake, cookie, or biscuit so tender that it feels like a mass of buttery crumbs just barely held together until they dissolve in your mouth.

Of course, now that your egg yolk is out of the shell, it's a bit late to boil it as a normal boiled egg. But you can poach an egg yolk in gently boiling water. The yolk has a sort of membrane that will keep it intact if you handle it gently. Here's a recipe for a soft poached egg yolk, but you will want to cook it until it's hard (maybe 5 minutes, but that's a guess).