How to Make It
Heat broiler. Place the bread and asparagus on a baking sheet. Drizzle with the oil and season with 1/2 teaspoon each salt and pepper.
Broil until the bread is toasted, 1 to 2 minutes per side; transfer the bread to plates. Continue broiling the asparagus, tossing once, until tender, 4 to 8 minutes more.
Meanwhile, bring a large saucepan of water to a boil. Carefully lower the eggs into the water. Reduce heat and gently simmer for 6 minutes. Cool under running water and peel.
Divide the asparagus among the toast, sprinkle on the Parmesan, and top with the eggs.