SET UP: Preheat the broiler to high with a rack set 4 inches from the heat source. Bring a large pot of salted water to a boil.
COOK THE GREENS: Add the broccoli rabe to the water and cook until crisp tender, 3 to 4 minutes, then drain. Heat the oil in a large skillet over medium-high heat until hot. Add the garlic and cook, stirring, until golden, 1 to 2 minutes. Stir in the broccoli rabe, season with salt and pepper, remove from the heat, and keep warm.
TOAST THE ROLLS: Melt 4 tablespoons of the butter in a large skillet. Brush the cut sides of the rolls with some of the melted butter. Broil the rolls, cut-side up, until brown, about 3 minutes. Divide the provolone among the rolls and broil until the cheese melts, about 1 minute. Fill the rolls with broccoli rabe.
FRY THE EGGS AND ASSEMBLE: Heat one more tablespoon butter in the same skillet over medium-high heat until hot. Stir in the Sriracha and simmer for 20 seconds. Working in batches and adding more butter if needed, crack the eggs into the skillet and fry until the whites just begin to set, about 1 minute. Cover the skillet and cook over low heat until the egg whites are set but the yolks are still runny, 1 to 2 minutes. Put 1 to 2 eggs on each sandwich, sprinkle with Parmesan, and serve.
Recipes from "The Chopped Cookbook: Use What you've Got to Cook Something Great" (c) Copyright 2014 by Television Food Network, G.P. By arrangement with Clarkson Potter/Publishers.