Cooking the rigatoni twice--first in boiling water and then in the red pepper stewing liquid--infuses it with sweet and rich pepper flavor.
Bring a large pot of salted water to a boil. Add the rigatoni and cook, stirring often, until barely al dente, about 10 minutes. Drain the pasta, reserving 1 1/4 cups of the cooking water.
Meanwhile, in a large enameled cast-iron casserole, melt the butter in the oil. Add the garlic and peppers, cover and cook over moderately high heat until fragrant, about 2 minutes. Add the warm water and a pinch of salt, cover and simmer over low heat until the peppers are tender, about 10 minutes.
Add the rigatoni and the reserved pasta cooking water to the peppers. Cover and cook over moderately low heat, stirring a few times, until the rigatoni is al dente and the sauce has thickened slightly, about 5 minutes longer. Discard the garlic. Stir in the basil and season with salt and pepper. Transfer to a large bowl and serve at once, passing the Parmesan cheese at the table.