Preheat the oven to 425 degrees . Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente.
Trim the bottoms of the bell peppers, without cutting a hole, so that they stand. Season inside with salt and black pepper. Turn the peppers bottom side up in a 9-by-13-inch baking dish, set the tops alongside and drizzle with EVOO. Roast for 20 minutes.
Using a food processor, puree the roasted red peppers. In a large skillet, heat 2 tablespoons EVOO, 2 turns of the pan, over medium heat. Add the red onion, garlic, mushrooms, crushed red pepper and rosemary and cook until softened, 7 minutes. Stir in the pureed peppers and the fire-roasted tomatoes; season with salt and black pepper. Simmer for 5 minutes. Add the pasta and toss. Add the arugula and basil and cook until wilted.
Preheat the broiler. Turn the peppers upright; fill with pasta. Top with the cheese and broil until melted, 2 minutes. Cover with the tops and serve with any extra pasta.