Preparation Have ready large bowl ice water. In medium saucepan over high heat, bring salted water to boil. Add asparagus and boil, uncovered, until crisp-tender, 2 to 3 minutes. Drain, then immediately plunge spears into ice water to stop cooking. Drain again and pat dry. Preheat grill to moderate heat. Transfer asparagus to large rimmed baking sheet and drizzle with 4 tablespoons olive oil. Toss to coat. Grill, in batches if necessary, until lightly charred, 8 to 10 minutes. Keep warm. Arrange oven rack in middle position and preheat oven to 400°F. Lightly oil muffin pan. Crack one egg into each muffin cup (there will be 4 empty cups). Place muffin pan in large roasting pan and add enough hot water to reach halfway up the sides of muffin pan. Bake until eggs are set but yolks are still runny, about 7 to 8 minutes. While eggs cook, arrange 4 asparagus spears in fan pattern on each of 8 plates. Sprinkle each plate with 1/2 teaspoon salt and 1/4 teaspoon pepper, then drizzle each with 1 teaspoon lemon juice. Drape 1 slice prosciutto atop asparagus on each plate. Using small offset spatula, carefully remove eggs from pan and place 1 atop each slice prosciutto. Drizzle with remaining 4 tablespoons olive oil and sprinkle with Pecorino Pepata and parsley. Cook's note:If you prefer, the asparagus can be baked instead of grilled. Skip the boiling step. Drizzle the raw asparagus with oil and bake it at 450°F on a large rimmed baking sheet until tender, about 10 minutes.
Preparation Have ready large bowl ice water. In medium saucepan over high heat, bring salted water to boil. Add asparagus and boil, uncovered, until crisp-tender, 2 to 3 minutes. Drain, then immediately plunge spears into ice water to stop cooking. Drain again and pat dry. Preheat grill to moderate heat. Transfer asparagus to large rimmed baking sheet and drizzle with 4 tablespoons olive oil. Toss to coat. Grill, in batches if necessary, until lightly charred, 8 to 10 minutes. Keep warm. Arrange oven rack in middle position and preheat oven to 400°F. Lightly oil muffin pan. Crack one egg into each muffin cup (there will be 4 empty cups). Place muffin pan in large roasting pan and add enough hot water to reach halfway up the sides of muffin pan. Bake until eggs are set but yolks are still runny, about 7 to 8 minutes. While eggs cook, arrange 4 asparagus spears in fan pattern on each of 8 plates. Sprinkle each plate with 1/2 teaspoon salt and 1/4 teaspoon pepper, then drizzle each with 1 teaspoon lemon juice. Drape 1 slice prosciutto atop asparagus on each plate. Using small offset spatula, carefully remove eggs from pan and place 1 atop each slice prosciutto. Drizzle with remaining 4 tablespoons olive oil and sprinkle with Pecorino Pepata and parsley. Cook's note:If you prefer, the asparagus can be baked instead of grilled. Skip the boiling step. Drizzle the raw asparagus with oil and bake it at 450°F on a large rimmed baking sheet until tender, about 10 minutes.