Bring a large pot of well-salted water to a boil.
Heat the oil and garlic in a 10-inch straight-sided sauté pan over medium heat until the garlic sizzles steadily for about 1 minute and just starts to brown around the edges. Add the roasted red peppers, thyme, and red pepper flakes and cook, stirring, for a couple of minutes to heat through. Add the chicken broth and sherry vinegar. Raise the heat to medium high and bring to a boil. Remove from the heat, let cool for a couple of minutes, and then transfer to a blender or food processor and purée.
Return the puréed pepper mixture to the sauté pan. Stir in the cream and 3/4 cup of the Parmigiano and bring to a boil. Remove from the heat and season with salt and pepper to taste.
Meanwhile, cook the rigatoni in the boiling salted water, stirring occasionally, until it’s just tender to the tooth (see the package for cooking time). Drain and add the pasta to the sauté pan. Cook over medium heat for 1 to 2 minutes, tossing and stirring, to blend the flavors and slightly thicken the sauce. Season with salt and pepper to taste.
Serve immediately, sprinkled with the remaining cheese and a few grinds of black pepper.