Heat oven to 450 degrees. Spread asparagus on a baking sheet and toss with olive oil, salt and pepper. Roast, shaking the pan occasionally, until the asparagus is lightly charred and tender, about 12 minutes. (You can let the asparagus sit at room temperature for hours, or refrigerate overnight.)
Beat the eggs with salt, pepper and half the cheese. Cut the asparagus into 2-inch lengths and arrange in a single layer in a 10-inch nonstick skillet. Drizzle with more olive oil and set over medium heat.
Pour the egg mixture over the asparagus. Use a spatula if necessary to make a round frittata. Cook until nearly set, tilting the pan and lifting the edge of the set egg to let the liquid egg flow underneath, about 4 minutes.
When the top is somewhat set, put it in the oven for a few minutes.
Sprinkle with the remaining cheese and serve hot, warm or at room temperature.