Break off the woody ends of the asparagus and peel the bottom half of the stalks with a vegetable peeler. Place on a baking sheet and drizzle with olive oil. Sprinkle with 1 teaspoon salt and ½ teaspoon pepper. Roast for 25 minutes, stirring once or twice.
Whisk together the melted butter, mayonnaise, and lemon juice. Drizzle the sauce over the roasted asparagus and top with sliced eggs. Sprinkle with a pinch of salt and pepper.