Preheat an oven to 425°F.

Place asparagus on a baking sheet, and drizzle with olive oil, salt and pepper. Roast until tender but not falling apart (about 12 minutes), shaking the pan halfway through. Let cool a moment then chop into bite-sized pieces.

Preheat a broiler to high.

Whisk together eggs, milk, 1 teaspoon kosher salt, Parmesan, herbs and a few turns of black pepper. Stir in asparagus.

Warm butter in a 10-inch oven-proof skillet over medium heat. Pour in eggs and scramble for 2 minutes. Let cook untouched for another 2 minutes until the edges set. Grate more Parmesan over the top, then pop under a high broiler. Cook until the top is firm and golden (about 2 minutes more).

Transfer frittata to a cutting board, cut in wedges and serve with more fresh herbs!