Preheat oven to 425 degrees. Line a heavy baking sheet with parchment paper.
In a heavy saucepan over medium heat, bring the milk, water, butter, and salt to a rolling boil, about 3 minutes. Add the flour all at once, and begin stirring quickly. Keep stirring until the dough begins to come together and pull away from the sides of the pan. This whole process should take no more than a minute or a minute and a half. Remove pan from heat, and let dough rest for 5 minutes.
Using a rubber spatula, spoon the dough into the bowl of an electric stand mixer fitted with the paddle attachment, and beat it on medium speed, adding the eggs, one at a time. (If the dough separates, don't fret; it will come back together.) After adding all the eggs, increase the mixer speed to high and beat in the Gruyere, the Parmesan, the mustard and the cayenne pepper for about 3 minutes. The dough should be shiny and sticky.
Using a measuring spoon, scoop the dough in one teaspoon increments onto the parchment-lined baking sheet, each mound approximately 2 inches apart. Note: You may want to prepare extra baking sheets, as you will have several batches of puffs.
Turn the oven down to 375 degrees. Place baking sheet in the oven and bake for 10 to 12 minutes. Rotate the pan and bake for another 6 to 8 minutes, until the tops are golden brown.
Remove from oven and let cool on the baking sheet for at least 5 minutes before serving. Or, let them cool completely and freeze. They will keep for up to 3 months in the freezer. Reheat the, covered, for 10 to 15 minutes at 350 degrees and serve warm.
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