Sauté garlic in hot oil in a 6-quart saucepan over medium heat 1 minute. Add tomatoes and tomato puree. Bring to a boil; reduce heat to low. Stir in red pepper flakes and next 4 ingredients; cook, stirring occasionally, 20 minutes.
Prepare pasta in a large Dutch oven according to package directions. Drain, reserving 1/2 cup cooking liquid. Return pasta and reserved cooking liquid to Dutch oven, and sprinkle with shredded cheese.
Stir basil into tomato sauce, and pour 3 cups sauce over pasta. Toss to coat. Serve with remaining sauce. Garnish, if desired.
*1/2 cup freshly grated Parmesan cheese may be substituted.