Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper or a silpat mat. Set aside.
With a serrated knife, cut the "lid" off the top of the bread. Gently tear out the insides of the loaf, leaving the loaf 3/4-inch around all sides to create a shell. Place the loaf on the prepared baking sheet, drizzle the inside with 2 teaspoons olive oil, and sprinkle with 1/4 teaspoon salt and 1/4 teaspoon pepper. Bake until lightly crispy, about 10 minutes. Place on a wire rack to cool while you prepare the eggs. Preheat the oven broiler.
In a medium bowl, thoroughly whisk together the eggs, remaining 1/4 teaspoon salt and 1/4 teaspoon black pepper. Be sure the eggs are completely beaten and slightly foamy. Set aside.
Heat 1 tablespoon olive oil in a large skillet over medium high heat. Remove the sausage from its casing, then crumble it into the skillet, breaking it up and cooking on all sides, until golden brown. With a slotted spoon, remove the sausage to a paper towel-lined plate. With an additional paper towel, carefully wipe the skillet clean.
Heat the remaining 1 tablespoon olive oil in the skillet over medium high. Once hot, add the onion and red peppers. Cook, stirring occasionally, until softened, about 6 minutes. Reduce the heat to medium, then stir in the basil and sausage. Carefully pour in the eggs and 2/3 of the mozzarella. Cook, stirring gently, until the eggs are just beginning to set, 1-2 minutes. (They will continue to cook a bit in the oven).
Return the bread bowl to the baking sheet. Fill with the egg mixture, then sprinkle the top with the Parmesan and the remaining mozzarella. Place in the oven and broil until the cheese is melted and bubbly and the eggs are just cooked through, about 3 minutes. Watch carefully so that the bread does not burn. Transfer to a cutting board and let rest for 2 minutes. Slice into wedges and enjoy warm.
This breakfast bowl recipe is best enjoyed the day its made but will last in the refrigerator for 1 or 2 days more. Reheat gently in a toaster or conventional oven.