2 tablespoons olive oil, divided
3 cups whole-wheat baguette or other crusty bread, cut into 1/2-inch cubes
1 small onion, diced
3 cups chopped broccoli (about 1/2 head), chopped into 1/2-inch pieces
6 large eggs
3/4 cup low-fat or whole milk
1 1/2 teaspoons Dijon mustard
1/2 teaspoon salt
1/2 teaspoon freshly ground black pepper
1/2 cup packed, shredded extra-sharp cheddar cheese
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.