Preheat oven to 500 degrees F. If using a pizza stone preheat for 1 hour. Alternatively, preheat a baking sheet placed upside down on the top rack for 10 minutes.
Prepare the toppings. Heat 2 tablespoon olive oil in a saute pan over medium heat. Saute the sliced bell pepper until softened, about 5 minutes. Add the balsamic vinegar and season with salt and pepper. Cook for another minute and remove from heat. Remove from heat and set aside.
Wipe the same skillet clean and cook the sausage until browned, breaking up the meat into bite-size pieces. Remove from heat, drain the excess oil, and set aside.
In the same skillet, saute the mushrooms until browned and caramelized, about 7 minutes. Season with salt and pepper. Remove from heat and set aside.
Dust a clean work counter with flour and use your hands to roll out the dough into a 12-inch circle, pushing from the center out. Spread the marinara sauce on the dough and top with sausage, roasted red bell pepper, mushrooms, and torn mozzarella.
Carefully transfer the pizza to the hot baking sheet. Turn off the oven and turn on the broiler to high. Broil the pizza for 2 minutes, then turn off the broiler and turn on the oven back to 500 degrees F. Continue to back for another 6-7 minutes or until the pizza is browned and the cheese is melted. Remove from the oven.
Toss the arugula with lemon juice, olive oil, salt, and pepper. Top the pizza with the arugula and serve immediately.