Heat olive oil in a large pot over medium heat. Sauté chopped onion for 5 to 7 minutes until softened, then add minced garlic, red bell pepper, and jalapeño; cook for another 2 minutes.
Add ground turkey or beef, breaking it up as it browns (about 7 to 10 minutes). Drain excess grease.
Stir in pumpkin puree, kidney beans, black beans, diced tomatoes, and broth. Add chili powder, cumin, oregano, cayenne pepper (if using), salt, and pepper.
Bring to a simmer over medium heat; reduce heat to low and cover. Let simmer for at least 30 minutes.
Taste and adjust seasonings; serve hot with desired toppings.