Ingredients

Active time 20 minutes, start to finish 25 minutes

1 1/2 pounds medium asparagus, trimmed and, if desired, peeled
2 1/2 tablespoons unsalted butter
2/3 cup freshly grated Parmigiano-Reggiano (2 ounces, see note)
4 large eggs

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 two 9 1/2-inch oval gratin dishes, about 2 1/2 inches deep, using 1/2 tablespoon butter total, then divide asparagus between them. Season with salt and black 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 black 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.
(Cook's warning: If eggs are served with runny yolks, they will not be fully cooked, which may be of concern if there is a problem with salmonella in your area.) Makes 2 servings.

Directions

Note: Parmigiano-Reggiano denotes cheese from Italy's prime Parmesan-producing region.