Snap off and discard woody bases from asparagus spears. In a covered medium saucepan cook asparagus in a small amount of boiling salted water for 3 to 5 minutes or until crisp tender. Divide asparagus among four serving plates, forming bundles.
In a large skillet melt 2 tablespoons of the butter over medium heat. Break eggs into skillet. Reduce heat to low; cook eggs for 3 to 4 minutes or until whites are completely set and yolks start to thicken. Place an egg on top of each asparagus bundle.
In a small saucepan melt the remaining 2 tablespoons butter; drizzle over asparagus. Sprinkle with salt and cracked black pepper. Sprinkle with Parmesan cheese.