Place the tomatoes and basil in a food processor or blender and pulse until smooth. Cook the pasta in salted, boiling water until tender, about 8 minutes. Meanwhile, place the oil in a very large skillet and set over medium-high heat. Add the asparagus and bell peppers and cook 2 to 3 minutes. Mix in the garlic and chili flakes and cook 1 minute more. Add the pureed tomato mixture, salt and pepper, bring to a simmer, and simmer 2 to 3 minutes.
When cooked, drain the pasta and reserve 1/2 cup of its cooking liquid. Add the pasta and reserved cooking liquid to the skillet and toss to combine. Sprinkle with freshly grated Parmesan cheese.