Heat broiler. Place peppers, skin side up, on a foil-lined baking sheet; broil 4 inches from heat until charred, 18 to 20 minutes. Transfer to a large bowl. Cover with plastic wrap; steam 2 to 3 minutes. Using a paper towel, rub off pepper skins, reserving any juices in bowl. Thinly slice peppers crosswise into 1/4-inch strips; return to bowl. Set aside.
In a large pot of boiling salted water, cook pasta until al dente, according to package instructions. Drain, reserving 1/2 cup pasta water.
Meanwhile, heat oil in a large skillet over medium heat. Cook sausage, breaking it up with a spoon, until browned, 7 to 10 minutes. Add roasted peppers; cook until heated through.
Transfer sausage mixture to bowl; add pasta, butter, reserved pasta water, and Parmesan. Season with salt and pepper. Toss to combine.
When cooking pasta, save a little of the cooking water before draining -- drizzling a little of it into the finished dish will improve the consistency of your sauce.