In a 3 ½ to 4-quart slow cooker, combine the rinsed cannellini beans, undrained stewed tomatoes, chopped sweet peppers, onion, minced garlic, Italian seasoning, and black pepper.
Pour the vegetable broth and white wine (or additional broth) over the mixture.
Cover and cook on low for 7 to 9 hours or on high for 3 ½ to 4 ½ hours.
Once cooked, use a slotted spoon to transfer the bean and vegetable mixture to a large serving bowl, making sure to reserve the cooking liquid in the slow cooker.
Stir the basil pesto directly into the bean mixture.
Towards the end of the cooking time, cook the penne pasta according to package directions until al dente.
Drain well.
Add the cooked pasta to the bowl with the bean and pesto mixture, tossing gently to combine.
Stir in the reserved cooking liquid, a little at a time, until the sauce reaches your desired consistency.
Serve immediately, sprinkled generously with Parmesan or Romano cheese.