Preheat oven to 350°F. Mist a 9-inch baking dish with cooking spray. Bring a pot of salted water to a boil. Add broccoli; cook for 4 minutes. Drain; rinse under cold water. Pat dry; transfer to baking dish.
Warm oil in a skillet over medium heat. Sauté onion for 3 minutes. Add garlic and mushrooms; sauté for 2 minutes. Raise heat to high; sauté for 3 minutes. Add to baking dish and season mixture with salt, pepper and red pepper.
Wipe out skillet; return to medium heat. Melt 2 T bsp. butter, then add flour. Cook, stirring, until smooth, 2 minutes. Whisk in milk; bring to a boil. Whisk for 5 minutes, until thickened. Add mustard; season with salt and pepper. Drizzle over broccoli mixture, spreading with a wooden spoon to cover
Melt remaining 1 Tbsp. butter. Combine bread crumbs and Parmesan. Stir in melted butter. Sprinkle mixture over casserole. Bake for 30 to 35 minutes, until bubbly and golden brown. Let sit for 5 minutes before serving.