Immediately transfer the dough to the stand mixer, fitted with the paddle attachment (or a large bowl if using a hand mixer).
Mix on low speed for a few minutes (i.e., until the steam stops rising) to release some of the heat from the dough. Begin to add the eggs one at a time and mix on medium speed. The amount of eggs needed to make this recipe will vary slightly due to the amount of moisture that was cooked off in the previous step and the size of the eggs. Incorporate each egg fully before adding the next to ensure that the mixture does not become too runny.
When adding the egg, the mixture will immediately begin to look curdled. After mixing for a few seconds, the dough should smooth out.
After adding two eggs, use a spatula to scrape the sides of the bowl to ensure all ingredients are thoroughly incorporated. Test the consistency of the dough by dipping the paddle attachment or a spatula into the dough, holding it above the bowl, and checking to see how the dough falls. If the consistency is correct, the dough should hang down from the paddle in a “V.”
If it doesn’t hold a “V,” more liquid is needed. Beat the remaining eggs and add small amounts at a time to the dough (i.e., don’t pour in an entire egg). Don’t add too much of the beaten eggs because you can turn the dough into “soup” (i.e., a very thin dough). Keep any remaining egg to use as an egg wash. If you used all of your eggs, beat the additional egg yolk and use for the egg wash. I did not need the additional yolk.