Preheat the oven to 400 degrees F. Line a baking sheet with parchment.
Heat the sausage in a large nonstick skillet over medium-high heat and cook, stirring to break up the sausage into small crumbles, until browned and no longer pink, about 10 minutes. Transfer the sausage to paper towels to drain and return the skillet to medium heat.
Heat the oil in the skillet, then add the mushrooms. Sprinkle with salt and pepper and cook, stirring, until golden brown, 8 to 10 minutes. Stir in the bell pepper and onions and cook, stirring, until lightly caramelized and soft, 6 to 8 minutes. Transfer the vegetables to a bowl and stir in the olives.
Roll the dough into a 20-by-14-inch rectangle on a lightly floured work surface. Starting on the shorter end of the dough, arrange the pepperoni slices, ham strips and cooked sausage evenly over half the dough, leaving a 1-inch border on the sides, then spoon the marinara sauce evenly over the meat. Sprinkle the mozzarella over the sauce, then scatter the cooked vegetables evenly over the cheese. Working from the short side, tightly roll the dough up, jelly roll-style, into a log. Pinch the open seams together to seal, then tuck them underneath the log.
Transfer the log to the prepared baking sheet, brush with the egg wash and sprinkle with the garlic powder. Bake until the bread is golden brown, about 40 minutes.
Let the bread cool for at least 10 minutes. Halve the bread lengthwise, cut each half crosswise into 4 equal pieces and serve warm.
To make rolling and shaping the dough easy, keep the dough refrigerated until 10 to 15 minutes before you are ready to use it.
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