Bring a large pot of water to a boil for the pasta.
Roast all the peppers over the flame on a gas stove or under a broiler on high with the door ajar until skins are charred. Place peppers in a bowl and cover until cool. Once cool peel and seed peppers, and chop.
If using fresh tomatoes, score the skins with an X on bottom and core them. Place the tomatoes in boiling water for 1 minute then dunk them in an ice bath and peel. Using a food mill, purée the tomatoes–you should yield about 3-4 cups of passata. You can also substitute about the same amount of store bought passata or crushed tomatoes.
Heat a large deep skillet or Dutch oven over medium heat with olive oil, 3 turns of the pan. Add chopped onions, sliced garlic, season with salt and pepper and cook partially covered to soften, stirring occasionally. Add tomatoes and stock, and simmer uncovered over medium-low heat to thicken a bit and allow the flavors to combine. Wilt in basil. When you drop the pasta, stir in about 1/3 cup cream to sauce, about 2 slow turns of pan in light stream, and reduce heat to low.
Cook pasta in salted water to al dente
. Add a ladle of starchy water to sauce just before draining then toss “riggies” with creamy sweet pepper sauce. Adjust salt and pepper, and serve in shallow bowls topped with freshly cheese.