Preheat oven to 375°F (190°C) and line a baking sheet with parchment paper.
In a large skillet over medium-high heat, brown the ground beef until cooked through, breaking it into small crumbles.
Add the diced bell peppers and onions to the skillet. Sauté for 5-7 minutes until vegetables are softened.
Stir in minced garlic, salt, pepper, and oregano. Cook for 1 additional minute, then remove from heat and drain excess fat.
Roll out the dough on a lightly floured surface into a 12x15 inch rectangle.
Spread the beef and pepper mixture evenly over the dough, leaving a 1-inch border on all sides.
Sprinkle the shredded mozzarella cheese over the beef layer.
Starting from the long side, tightly roll the dough into a log and pinch the seams to seal.
Place the roll seam-side down on the prepared baking sheet.
Brush the top with the beaten egg evenly to create a glaze.
Bake for 25-30 minutes, or until the bread is deep golden brown and firm to the touch.
Allow to rest for 10 minutes before slicing into 2-inch rounds.