Preheat the broiler. Toss the asparagus with 2 tablespoons olive oil, 1/2 teaspoon salt and a few grinds of pepper on a baking sheet; spread in a single layer. Broil, stirring occasionally, until tender, 4 to 6 minutes. Let cool slightly.
Bring a saucepan of water to a boil. Add the egg and reduce the heat; simmer 5 minutes. Drain and transfer to a bowl of ice water.
Peel the egg and transfer to a blender. Add the garlic, lemon juice, parmesan and mustard and puree until smooth. With the machine running, drizzle in the remaining 8 tablespoons olive oil and blend until thick and creamy. Stir in the crushed peppercorns. Spoon the lemon-pepper sauce over the asparagus and top with more parmesan.