Heat olive oil in a large skillet or Dutch oven over medium-high heat. Add the sausage, breaking it up, and cook until browned and no longer pink, about 5 to 7 minutes. Remove with a slotted spoon and set aside.

Add the onion to the pan and cook until softened, 3 to 4 minutes. Stir in garlic and cook 30 seconds.

Mix in tomato paste and cook 1 to 2 minutes. Pour in broth and cream, whisk, and bring to a gentle simmer.

Return sausage and pasta to the pan. Stir, reduce heat to medium, and simmer, stirring occasionally, until pasta is al dente and sauce thickens, 12 to 15 minutes. Add a splash of warm water if the pan looks dry.

Remove from heat. Stir in Parmesan, season with salt and pepper. Spoon into bowls and top with basil.