3/4 cup water
1/3 cup unsalted butter
3/4 teaspoon coarse salt
3/4 cup all-purpose flour
5 large eggs, at room temperature
3/4 cup grated Gruyere cheese (about 2 1/2 ounces)
Preheat the oven to 375F. Line a baking sheet with a silicone baking sheet or parchment paper. To make the dough, in a medium saucepan, bring the water, butter, and 1/2 teaspoon of the salt to a boil over high heat. Immediately remove the pan from the heat, add the flour all at once, and beat vigorously with a wooden spoon until the mixture is smooth and pulls away from the sides of the pan to form a ball, 30 to 60 seconds. (This mixture is called the panade.) Beat the mixture over low heat for an additional 30 to 60 seconds to dry the mixture. To make the egg wash, whisk 1 of the eggs in a small bowl with the remaining 1/4 teaspoon salt until well mixed; set aside. With a wooden spoon, beat the remaining 4 eggs into the dough, one at a time, beating thoroughly after each addition. (It will come together, I promise.) Beat until the dough is shiny and slides from the spoon. Add the grated cheese. If using parchment paper to line the baking sheet, glue down the paper at this point with a few dabs of the dough. To form the gougeres, use either a tablespoon for a rustic look, or for a more finished appearance, a pastry bag fitted with a 1/2-inch round tip. Spoon or pipe 12 mounds of dough about 2 inches in diameter onto the baking sheet, spacing them at least 2 inches apart. Brush the puffs with the reserved egg wash. Bake until puffed and golden, 25 to 30 minutes. To test for doneness, remove one puff from the baking sheet and let it cool for 45 to 60 seconds. If it remains crisp and doesnt deflate, it is done. If not, return it to the oven and continue baking 5 to 10 minutes more. Remove to a rack to cool. Let the puffs cool slightly on the sheet, then transfer to a cooling rack. Serve warm or at room temperature. These are brilliantly resilient and freeze beautifully. Once cooled, store them in an airtight container in the freezer for up to 4 weeks. Warm and re-crisp in a 350F oven, 5 to 7 minutes. To make 30 to 35 medium puffs, adjust the ingredient amounts as follows: 1 1/4 cups flour, 1 cup water, 3/4 teaspoon salt, 6 1/2 tablespoons butter, 5 eggs, and 1 cup cheese.