Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch baking dish with 2 teaspoons butter and set aside.

Melt 2 teaspoons butter in a medium-sized skillet over medium-high heat. Add onions, green and red bell peppers, 1 teaspoon black pepper, garlic powder, and 1/4 teaspoon salt. Cook, stirring, until vegetables are soft, 5 to 7 minutes. Add parsley, stir, and remove from heat. Let vegetables cool.

Heat a medium-sized skillet over medium heat. Cook and stir sausage in the hot skillet until lightly browned, 5 to 7 minutes. Drain sausage on a plate lined with a paper towel.

Beat eggs in a large bowl. Add milk, half-and-half, Italian seasoning, remaining 1 teaspoon pepper, and remaining 1/4 teaspoon salt and whisk to combine. Add bread cubes and let sit for 5 minutes. Add cooked sausage, bacon, vegetables, Cheddar cheese, 1/2 cup bread crumbs, and 1/2 cup Parmesan cheese and stir to incorporate. Spoon mixture into prepared baking dish and cover with aluminum foil.

Bake in the preheated oven until almost set, 50 to 55 minutes.

Combine remaining 1/2 cup bread crumbs, remaining 1/2 cup Parmesan cheese, 2 tablespoons melted butter, and remaining 1/2 tablespoon Italian seasoning in a small bowl. Remove pudding from oven, leaving oven on. Uncover and sprinkle bread crumb mixture evenly over the top. Return to the oven and increase heat to 375 degrees F (190 degrees C). Continue baking until pudding is completely set in the center, puffed, and golden brown on top, about 20 minutes more.

Remove from oven and allow to stand for 10 to 15 minutes before serving.