In a large skillet, heat oil on medium for 30 seconds.
Add scallions, salt, and ¼ tsp black pepper.
Cook for 3 minutes.
Add garlic, bell peppers, and broccoli and cook for 7 minutes.
Coat a 9-by-13-inch baking dish with cooking spray.
Line with English muffins.
Top with vegetable mixture, Monterey Jack, and ½ cup cheddar.
In a large bowl, whisk eggs, milk, and mustard.
Add ¼ tsp pepper.
Pour eggs over vegetables and cheese.
Cover with foil and refrigerate for 4 hours for overnight.
Preheat oven to 350°.
Bake strata, covered, for 30 minutes.
Remove foil and sprinkle with ½ cup cheddar.
Bake for 25 minutes more or until golden brown and set in center.
Cool for 10 minutes.