Cut bell peppers in half lengthwise; discard seeds and membranes. Place pepper halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil 8 minutes or until blackened. Place peppers in a zip-top plastic bag; seal. Let stand 20 minutes. Peel; place peppers in a blender.
Heat 2 teaspoons oil in small skillet over medium heat. Add garlic; sauté 1 minute. Remove from heat; let stand 5 minutes. Add garlic mixture, remaining 1 tablespoon oil, broth, and next 5 ingredients (through red pepper) to blender with peppers; process until smooth. Combine bell pepper mixture and basil with pasta. Sprinkle with cheese.
Wine note: A simple pasta dish doesn't need a superpricey wine. Instead, I like to take a tip from Italian trattorias and serve a simple, bracingly fresh white like pinot grigio. It's the ultimate no-frills, no-fuss wine, and its light citrus/almond/hay notes are great with goat cheese. Try Lagaria 2004 pinot grigio from Delle Venezie, Italy ($9). -Karen MacNeil