Preheat oven to 450 F. In 10-inch ovenproof skillet over medium heat, heat 1 tablespoon oil. Add bread to skillet and cook, tossing frequently, until golden brown, about 6 minutes. Transfer bread to plate and carefully wipe crumbs out of pan.

Add remaining oil to skillet then add onion and cook until softened slightly, 2 minutes. Add broccoli and cook, stirring frequently, until it begins to soften, 3 minutes.

In medium bowl, whisk eggs, milk, mustard, salt and pepper. Add cheese and bread; toss to combine then pour bread mixture over vegetables in skillet.

Cover with foil and bake 10 minutes then uncover and continue baking until strata is set in center, 5-8 minutes. Remove from oven and let sit 5 minutes.

To serve, scoop out portions with large spoon or cut into wedges.