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1
Preheat the oven to 400.
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2
Line 2 large baking sheets with parchment paper.
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3
In a medium saucepan, combine the water with the butter, cayenne, cup of the milk and 1/4 teaspoon of the salt and bring to a boil.
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4
Add the flour and baking powder and cook over moderate heat, stirring constantly with a wooden spoon, until the dough pulls away from the side of the pan, about 2 minutes.
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5
Transfer the dough to the bowl of a standing mixer fitted with the paddle.
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6
Add 1 cup of the cheese and mix at medium speed until the dough cools slightly, about 1 minute.
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7
Add the eggs one at a time, mixing well between additions.
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8
After all the eggs have been added, mix the dough until shiny, about 5 minutes.
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9
Using a pastry bag, pipe the dough into 1-inch mounds about 1/2 inch high on the prepared baking sheets.
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10
Gently brush the gougeres with the remaining 2 tablespoons of milk and sprinkle with the remaining 1/4 teaspoon of salt and cup of cheese.
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11
Bake for about 8 minutes, until puffed.
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12
Rotate the baking sheets from top to bottom and back to front and bake for about 12 minutes longer, until the gougeres are golden brown.
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13
Serve hot or warm.
