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1
Preheat the oven to 350u00b0. Butter a baking sheet or line with parchment paper. (I used one half sheet pan and one quarter sheet pan because I could not fit all 8 pastries on the half sheet pan.)
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2
Combine the milk, butter, and salt in a heavy saucepan and cook over medium heat until the butter melts and the mixture comes to a full boil. (Do not use whole milk, or the gougeres will collapse. If you have only whole milk, use half milk and half water.) Add the flour all at once, stirring vigorously with a wooden spoon. Keep stirring until the mixture has formed a smooth mass and pulls away from the side of the pan and some of the moisture has evaporated. This will take about 3 minutes.
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3
Transfer the paste to a heatproof mixing bowl or the bowl of a stand mixer fitted with the paddle attachment. Add 5 of the eggs, one at a time, incorporating each egg before adding the next. (If using a stand mixer, mix on medium; if working by hand, use a wooden spoon.) When all the eggs have been added, the mixture will be very thick, smooth, and shiny. Use a rubber spatula to mix in the cheese, pepper, and thyme.
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4
Make the egg wash: whisk the remaining egg together with a pinch of salt in a small bowl. Use a large spoon to form 3-inch rounds about 1 inch high on the prepared baking sheet, spacing them about 2 inches apart. Brush with the egg wash and sprinkle with grated cheese. Baked until they have puffed, are light for their size, and are golden brown, 35-45 minutes.
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5
When they come out of the oven, poke a small hole in the side of each pastry to allow steam to escape (this should prevent them from collapsing). If splitting and filling, allow the gougeres to cool to room temperature first. Otherwise, serve hot, warm, or at room temperature.
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6
You can use this recipe to make classically small gougeres, too: just use a spoon to drop the dough into 1-inch mounds spaced 1 1/2 inches apart and bake for about 25 minutes. Small gougeres need not be slit when they come out of the oven to avoid collapsing.
