Step 1In a large saucepan, heat the butter, milk, salt, piment d'Espelette and nutmeg together over low heat until the butter has melted completely. Add the flour, stirring vigorously until the mixture forms a paste, then cook, stirring and smearing the dough constantly, until the mixture starts to smell nutty and small beads of fat form on the surface of the dough that's just come off the bottom of the pan, about 10 minutes total. (I usually stop stirring when my arm hurts too much to continue. It will be thick, like sugar cookie dough.)
Step 2Transfer the dough to the bowl of a stand mixer fitted with the paddle attachment and set aside until the dough has almost reached room temperature, about 15 minutes. Meanwhile, heat the oven to 425 degrees. Line two baking sheets with parchment paper and set them aside.
Step 3When the dough has cooled, with the machine on medium speed, add the eggs one at a time, mixing until the batter re-forms between each egg and scraping down the sides of the bowl as necessary. When you have added all the eggs, mix in the Gruyère and Parmesan on low speed.
Step 4Using two spoons, form the batter into golf ball-sized balls and arrange them on the prepared baking sheets about 1½ inches apart, dipping the spoons into a bowl of warm water between each one to keep the dough from sticking. Sprinkle the gougères liberally with the sea salt.
Step 5Bake the gougères for 10 minutes. Without opening the oven door, reduce the temperature to 350 degrees and continue to bake for 25 more minutes, or until the gougères are brown and crisp on the outside and half hollow in the center.
Step 6Serve immediately, or set aside to cool on racks no more than a few hours before serving.