Heat oil over medium-high heat. Remove sausage from casings and add to pan, breaking up with a wooden spoon. Cook until browned, about 3 minutes, continuing to break up the sausage. Add garlic and cook until fragrant, about 30 seconds. Add tomatoes and pepper; cover and cook for 2 minutes. Remove cover and use a wooden spoon to mash the tomatoes. Cover pan, reduce heat to low, and cook for 3 minutes. Remove pan from heat; add drained linguine, reserved pasta water, and arugula; toss together. Serve with shaved Parmesan on top.