Prepare a grill. Bring a large pot of salted water to a boil.
Toss tomatoes in oil in a large bowl. Put tomatoes on grill, reserving oil. Cover grill and cook tomatoes, turning occasionally with tongs, until skins are charred and flesh is softened, about 15 minutes.
While tomatoes are grilling, cook rigatoni in boiling water according to package directions, stirring often, until al dente. Drain.
Return tomatoes to bowl with oil. Use tongs to pull off skin, then coarsely mash tomato flesh. Stir in cream. Add cooked pasta, salt, pepper and parsley. Toss well. Serve with Parmesan cheese.