Bring a large pot of salted water to a boil. Cook rigatoni according to package directions. Reserve 1 cup pasta water, then drain.
While pasta cooks, heat 1 tbsp olive oil in a large skillet over medium-high heat. Add sausage and break up with a spoon. Cook until browned, about 6 minutes. Remove to a plate.
Add remaining 2 tbsp olive oil to the pan. Add cherry tomatoes cut-side down. Cook without stirring for 3 minutes until they start to blister.
Add garlic and red pepper flakes. Cook 1 minute.
Pour in wine and scrape up any browned bits. Let it bubble for 2 minutes.
Return sausage to the pan along with cooked pasta. Toss everything together, adding pasta water a little at a time until sauce coats the noodles.
Remove from heat. Stir in basil and half the parmesan. Serve with remaining parmesan on top.