In a large saucepan, heat the olive oil over medium heat. Add the carrot, onion and celery and cook, stirring, until tender, 6 to 8 minutes. Stir in the garlic and 1/2 teaspoon salt. Add the tomatoes and basil and bring to a simmer. Using a food processor, puree the tomato mixture.
In a large pot of boiling, salted water, cook the pasta until al dente; drain. Meanwhile, in a medium skillet, melt the butter over medium heat. Add the rosemary and cook, stirring, for 1 minute. Add the pureed sauce, the cream and crushed red pepper; season with salt. Cook, stirring occasionally, until thickened, about 10 minutes. Toss with the pasta.