- 1 1/2 pound medium asparagus, trimmed and, if desired, peeled
- 2 1/2 tablespoons unsalted butter
- 2/3 cup freshly grated Parmigiano-Reggiano (2 oz)
- 4 large eggs
- Set oven rack in upper third of oven, then preheat oven to 425°F.
- Cook asparagus in a large deep skillet of boiling salted water until crisp-tender, about 4 minutes. Transfer with tongs to paper towels to drain.
- Generously butter gratin dishes using 1/2 tablespoon butter total, then divide asparagus between them. Season with salt and pepper, then sprinkle with half of cheese.
- Heat remaining 2 tablespoons butter in a 10-inch nonstick skillet over moderately high heat until foam subsides, then fry eggs, seasoning with salt and pepper, until whites are barely set, about 2 minutes.
- Carefully transfer 2 eggs to each gratin dish with a slotted spatula, placing on top of asparagus. Sprinkle eggs with remaining cheese and drizzle with any butter remaining in skillet.
- Bake in upper third of oven until cheese is melted and eggs are cooked as desired, 4 to 5 minutes for runny yolks.