In a 3. 5- or 4-quart slow cooker, combine the undrained diced tomatoes, rinsed and drained garbanzo beans, rinsed and drained kidney beans, tomato sauce, chopped onion, sweet pepper, chili powder, minced garlic, oregano, and cayenne pepper.
Stir everything together until well combined.
Cover the slow cooker and cook on the LOW setting for 5 to 6 hours or on the HIGH setting for 2. 5 to 3 hours, until the chili is fragrant and the vegetables are tender.
About 20 minutes before serving, cook the wagon wheel pasta in a separate pot according to package directions until al dente.
Drain well.
Serve the hot bean chili generously over the cooked pasta and sprinkle with shredded vegan cheddar-style cheese.
Adjust the heat to your liking! For a milder chili, use 2 teaspoons (10 ml / 0.3 fl oz) of chili powder and omit the cayenne. For more kick, add a pinch of red pepper flakes or a finely chopped jalapeño.