Dice the yellow onion and red bell pepper into evenly sized pieces, then mince the garlic. Drain and rinse the black beans and kidney beans in a fine-mesh strainer. Open the pumpkin puree and diced tomatoes, keeping the tomato juices. Measure the broth and seasonings before turning on the heat so the ingredients are ready to combine.
Heat the olive oil in a 12-inch (30 cm) skillet over medium heat. Add the diced onion and red bell pepper and cook for 4 minutes, stirring occasionally. The onion should begin turning translucent, and the pepper should soften slightly. This initial cooking releases moisture and develops a sweeter vegetable base.
Add the ground turkey to the skillet with the vegetables. Increase the heat to medium-high and cook for approximately 6 minutes, breaking the turkey into small crumbles with a wooden spoon. Add the minced garlic during the final minute and stir until fragrant. The turkey should lose its pink color, and most visible liquid should evaporate. Confirm the meat reaches 165°F (74°C) with an instant-read thermometer.
Transfer the cooked turkey, onion, bell pepper, and garlic to the 6-quart (5.7 L) slow cooker. Add the pumpkin puree, diced tomatoes with their juices, drained black beans, drained kidney beans, and chicken broth. Stir thoroughly until the pumpkin is evenly incorporated and no large patches of thick puree remain.
Sprinkle the chili powder, ground cumin, smoked paprika, salt, black pepper, and cinnamon over the chili mixture. Stir until the seasonings are evenly dispersed throughout the sauce. The mixture should look thick, reddish-orange, and evenly speckled with beans and turkey.
Cover the slow cooker with its fitted lid and cook on LOW for 6 hours. Keep the lid closed during cooking to preserve heat and moisture. By the end, the vegetables should be tender, the beans heated throughout, and the sauce thick enough to coat a spoon. The center of the chili should reach at least 165°F (74°C).
Remove the lid after the cooking cycle and stir gently from the bottom, incorporating any thicker pumpkin mixture into the sauce. The chili should have a cohesive, spoonable consistency rather than separate watery liquid and solids. If it appears thicker on the edges, stirring will redistribute moisture without breaking down the beans.
Use a ladle to divide the hot chili evenly among serving bowls. Each serving should contain ground turkey, both types of beans, and softened vegetables suspended in the thick pumpkin-tomato sauce. Serve while hot, with a balanced smoky aroma and a rich, lightly sweet finish.