Add 2 tablespoons of olive oil into a large skillet.
Add the sliced and seeded bell peppers, along with the peeled and sliced onion.
Cook over medium/high heat (stirring occasionally) for 7-10 minutes, or until the peppers are nicely soft and the onions are lightly caramelized. Set aside until ready to use.
Caramelized onions and bell peppers may be made in advance and kept in the refrigerator for 4-5 days.
Preheat oven to 375-degrees Fahrenheit.
Rip and tear 6-7 brioche buns into bite-sized pieces, and lay them in a single layer on a baking sheet.
Bake the bun pieces for 30 minutes to toast. Remove them from the oven and gently stir. Return them to the oven for an additional 15-20 minutes until they turn golden brown. Set aside to cool.
Meanwhile, remove the sliced Italian beef from the container (reserving the gravy at the bottom of the container). Using a chef's knife or santoku, chop the Italian beef into bite-sized pieces. Set aside.
In a large bowl, whisk together 4 eggs, salt, pepper, and the gravy remaining in the container (approximately 4 cups) until thoroughly combined.
Spray a 13x9 baking dish with cooking spray and layer the toasted brioche bun pieces evenly into the bottom of the casserole dish.
Top the layer of toasted brioche with the prepared chopped Italian beef, and then ladle the egg/gravy mixture evenly over the top of the beef.
If using, layer the caramelized onions and green pepper strips over the beef and gravy mixture and top the entire savory bread pudding with an even thick layer of shredded mozzarella cheese.
Top the casserole evenly with the garlic powder, dried basil, and dried oregano.
Bake in a preheated 350-degree Fahrenheit oven for 50-60 minutes, or until the center is set and the cheese is melted.
Cool for at least 15 minutes before serving, and enjoy!