1. In a large skillet over medium-high heat, warm oil. Add scallions, sprinkle with salt and sauté until tender, about 2 minutes. Add garlic, bell pepper and broccoli; cook, stirring often, until all vegetables are tender, about 5 minutes. Transfer to a bowl and season with salt and pepper.
2. Mist a 9-by-13-inch baking dish with cooking spray. Arrange English muffin pieces on bottom of dish, cut sides up. Scatter vegetable mixture over muffins, and sprinkle with 2 cups cheese.
3. In a large bowl, whisk together eggs, milk, mustard and hot sauce, if desired; season generously with salt and pepper. Pour egg mixture evenly over mixture in baking dish. Cover with plastic wrap and refrigerate for at least 4 hours or overnight.
4. Let strata stand at room temperature for 30 minutes before baking. Preheat oven to 375ºF; line a large rimmed baking sheet with foil. Remove plastic wrap from baking dish and cover with foil. Place dish on baking sheet; bake for 30 minutes. Remove foil, sprinkle with remaining 1/2 cup cheese; bake until golden and just set in center, 20 to 30 minutes longer. Let stand on a wire rack for 10 minutes before serving.