Cut the asparagus into 1/4-inch lengths. Bring a medium saucepan of salted water to a boil over medium-high heat. Add the asparagus and simmer until just tender, about 1 minute. Drain immediately and reserve.
In a heavy saucepan, bring the milk and butter to a boil over medium-high heat. In the meantime, sift together the 1/2 teaspoon salt, flour, and cayenne. As soon as the milk comes to a boil and the butter has melted, remove the pan from the heat and add the flour mixture all at once. With a wooden spoon, beat the mixture until it thickens and pulls away from the sides of the pan, about 1 minute. Transfer the mixture to a bowl. Add the eggs, 1 at a time, beating well after each addition. Do not add another egg until the previous one has been thoroughly incorporated. Let cool for 10 minutes.
Preheat the oven to 400°F. Line 2 baking sheets with lightly buttered parchment paper.
Add the asparagus, sheep's milk cheese, and Parmigiano to the dough and mix together. Spoon rounded teaspoons of the dough 1 inch apart onto the baking sheets. Bake in the middle of the oven until golden brown, 20 to 25 minutes. Remove the puffs from the parchment and serve immediately.