Rinse clean the asparagus. Cut off the "woody" ends of the asparagus and discard. Using a vegetable peeler, peel each stalk half way.
Lay the asparagus spears out in a single layer in a baking dish or a foil-covered roasting pan. Drizzle olive oil over the asparagus spears and then roll them back and forth until they are all covered with a thin layer of olive oil. Sprinkle with salt.
Place pan in oven and cook for approximately 10–12 minutes, depending on how thick your asparagus spears are, until lightly browned and tender when pierced with a fork.
While the asparagus cooks, use a blender or mini food processor to mix the egg yolk, lemon juice, cayenne pepper, and salt. Heat the butter in the microwave until melted. With the blender running, slowly add the melted butter to the blended egg to make a smooth, creamy sauce. Use the sauce immediately, add a tiny bit of warm water if it's too thick.
Place the asparagus on a plate and drizzle the sauce across the spears in the opposite direction.