In a large skillet over medium heat, cook oil, green onion, garlic, and broccoli. Cook, stirring often, until all vegetables are tender, about 5 minutes. Transfer to a bowl and season with salt and pepper.

Add red peppers to the veggies and stir to combine.

Spray a 9-by-13-inch baking dish with cooking spray. Arrange toasted English muffin pieces on bottom of dish with the cut sides up.

Spoon the reserved vegetable mixture over English muffins, and sprinkle with 2 cups cheese.

In a large bowl, whisk together eggs, milk, mustard. Season with salt and pepper and pour egg mixture evenly over mixture in baking dish.

Cover with plastic wrap and refrigerate for at least 4 hours or overnight.

Before baking, let strata stand at room temperature for 30 minutes before baking.

Preheat oven to 375ºF.

Remove plastic wrap from baking dish and cover with foil. 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. Serves 8.