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1
Bring the milk, butter, salt, and cayenne to a boil in a saucepan.
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2
Remove from the heat, add the flour all at once, and mix vigorously with a wooden spatula until the mixture forms a ball.
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3
Return the pan to the heat and cook over medium heat, stirring occasionally, for about 1 minute to dry the mixture a bit.
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4
Transfer to the bowl of a food processor, let cool for 5 minutes, then process for about 5 seconds.
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5
Add the eggs and paprika to the processor bowl, and process for 10 to 15 seconds, until well mixed.
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6
Transfer the choux paste to a mixing bowl, and let cool for 10 minutes.
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7
Preheat the oven to 375.
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8
Line a cookie sheet with a reusable nonstick baking mat or parchment paper.
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9
Reserve 1 tablespoon of the grated Parmesan cheese, then add the remainder and all the Swiss cheese to the choux paste.
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10
Stir just enough to incorporate.
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11
Using a tablespoon, scoop out a level tablespoon of the gougere dough, and push it off the spoon onto the cooking mat.
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12
Continue making individual gougeres, spacing them about 2-inches apart on the sheet.
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13
Sprinkle a few grains of coarse salt and a little of the reserved Parmesan cheese on each gougere.
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14
Bake for about 30 minutes, until nicely browned and crisp.
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15
Serve lukewarm or at room temperature with drinks.
