1. Preheat broiler to high.
2. Cook pasta according to package directions until al dente, omitting salt and fat. Drain pasta, reserving 1/4 cup cooking liquid.
3. While pasta cooks, place bell peppers, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil 8 minutes or until blackened. Wrap peppers in foil. Let stand 10 minutes; peel. Set aside half of 1 of each color bell pepper. Puree remaining peppers in a food processor.
4. Heat a large skillet over medium-low heat. Add oil to pan; swirl. Add garlic; cook 2 minutes or until fragrant and soft, stirring occasionally. Add reserved 1/4 cup cooking liquid, pureed bell pepper, salt, and black pepper; stir with a whisk. Simmer 5 minutes or until thickened. Add pasta; cook 1 minute, tossing to combine.
5. Thinly slice reserved bell pepper. Place about 1 cup pasta mixture in each of 4 bowls; top each serving with sliced bell peppers, 1 tablespoon basil, and 1 ounce cheese. Serve immediately.