Step 1Break the tough ends off the asparagus and place the spears in a medium skillet with enough water to cover the bottom of the pan. Bring to a simmer. Cover and cook until the asparagus is tender enough to puree, 10 to 15 minutes. Drain the asparagus, cover and keep warm.
Step 2Slice the rolls in half crosswise. Brush the cut sides with about 2 tablespoons of the melted butter. Toast the bread in a nonstick skillet over medium-low heat until browned on one side, about 1 minute, then turn to brown the second side. Repeat until all the bread is toasted. Keep warm.
Step 3Spray the bottom of a large skillet with nonstick spray, or use a nonstick skillet. Fill the skillet 3/4 full with water and bring to a boil.
Step 4Meanwhile, blend the egg yolks on high in a blender and add the lemon juice. While the blender is running, slowly drizzle in the remaining melted butter until incorporated and the sauce has thickened. Cut 6 stalks of the asparagus into 1-inch pieces. Add to the sauce and blend until pureed and the sauce has become light. Place the sauce in a bowl and stir in the prosciutto. Add salt and cayenne pepper to taste. Keep warm.
Step 5Reduce the boiling water to a simmer. To poach the eggs, work with 2 at a time. Crack the first egg into a small bowl, then carefully pour into the water; repeat with the second egg. Cook until the whites of the eggs are set and cooked through, about 3 to 4 minutes, then remove them from the water with a slotted spatula. Repeat with the remaining eggs. Place 1 egg on each slice of brioche. Spoon about 1 tablespoon of the hollandaise sauce over each egg. Sprinkle with the chives. Serve a wedge of avocado and any remaining asparagus spears alongside.