Heat the olive oil in a large pot or Dutch oven over medium heat. Add the diced onion and bell pepper. Sauté for about 5 to 7 minutes until the vegetables are softened. Stir in the minced garlic and cook for another minute until fragrant.
Add the ground turkey or beef to the pot. Use a wooden spoon to break the meat into small crumbles. Cook until the meat is fully browned and no longer pink. If there is excess grease, carefully drain it from the pot before moving to the next step.
Sprinkle the chili powder, cumin, smoked paprika, salt, and pepper over the meat and vegetable mixture. Stir well to coat everything in the spices. Letting the spices toast for a minute with the meat helps to release their full flavor profile.
Stir in the pumpkin puree, crushed tomatoes, black beans, kidney beans, and broth. Mix thoroughly until the pumpkin is completely integrated into the liquid. The mixture will look thick and rich at this stage.
Bring the chili to a gentle boil, then reduce the heat to low. Cover the pot and let it simmer for 20 to 25 minutes. Stir occasionally to prevent any sticking at the bottom. This simmering time allows the pumpkin to soften the acidity of the tomatoes and create a deep, complex flavor.