Bring a large pot of salted water to a boil. Add the pasta and cook according to the package instructions until al dente, then drain, reserving ⅓ cup of the pasta cooking water.
Meanwhile, in a large skillet over low heat, melt together the butter and olive oil until beginning to bubble. Add the garlic and shallot and cook until golden, 2–3 minutes. Add the red pepper flakes and tomato paste and stir until evenly incorporated.
Add the tomato sauce and heavy cream and stir the sauce for 2–3 minutes, until smooth and warmed through.
Add half of the basil and the cooked pasta and stir to coat in the sauce, then add ½ cup of Parmesan cheese and stir until incorporated and melted. If the sauce is too thick, add some of the reserved pasta water. Season with salt and pepper to taste.
Divide the pasta between bowls and garnish with the remaining basil and Parmesan cheese. Serve immediately.