Combine beans, undrained tomatoes, the sweet peppers, onion, Italian seasoning, black pepper, and garlic in a 3-1/2- or 4-quart slow cooker. Pour vegetable broth and wine over all.
Cover; cook on low-heat setting for 7 to 9 hours or on high-heat setting for 3-1/2 to 4-1/2 hours. Transfer bean mixture to a very large serving bowl using a slotted spoon, reserving cooking liquid. Stir pesto into bean mixture.
Meanwhile, cook pasta according to package directions; drain. Add pasta to bean mixture; gently toss to combine, adding enough of the liquid to make mixture of desired consistency. Sprinkle each serving with Parmesan cheese.
To serve, spoon pasta mixture into individual pasta bowls; sprinkle with cheese. Makes 6 to 8 servings.