1. Preheat oven to 400 degrees. Lightly butter an 8×8 inch square baking dish.
2. Combine the diced bread, broccoli, peppers and onions in the prepared baking dish, tossing to distribute evenly.
3. In a medium bowl, whisk together eggs, milk, cheese, salt, and pepper until well mixed. Pour evenly over the bread mixture.
4. Bake the strata at 400 degrees for 30-40 minutes, until golden brown and puffed, and a tester inserted into the center comes out clean.