Heat the olive oil in a large pot or Dutch oven over medium heat. Add the diced onion, garlic, bell pepper, and jalapeño (if using). Sauté for 5-7 minutes until the vegetables are softened.
Add the ground turkey to the pot and cook until no longer pink, breaking it up with a spoon as it cooks. Season with salt and pepper.
Stir in the chili powder, cumin, smoked paprika, and cinnamon, and cook for 1-2 minutes until fragrant.
Add the pumpkin puree, black beans, kidney beans, diced tomatoes, and chicken broth. Stir to combine.
Bring the chili to a simmer, then reduce the heat to low. Cover and let it simmer for 20 minutes, stirring occasionally, until the flavors meld together and the chili thickens.
Taste and adjust seasoning with more salt, pepper, or spices as needed.
Serve the chili hot, topped with your favorite toppings like chopped cilantro, sour cream, shredded cheese, avocado, and lime wedges.