Heat olive oil in a large pot over medium heat; cook and stir onion until slightly softened, 3 to 4 minutes. Add green bell pepper, yellow bell pepper, jalapeno, and garlic; cook until tender, 5 to 8 minutes.
Stir turkey into the pot and cook until evenly browned, about 5 minutes. Remove from heat and carefully drain off excess grease. Pour 1 can black beans, pumpkin, and tomatoes over the turkey mixture. Drain the second can of beans and add to the pot.
Mix chili powder, ground chipotle pepper, black pepper, and salt into the pot. Simmer chili, stirring every 5 to 8 minutes, until flavors combine, about 30 minutes. Top each serving with sour cream, Cheddar cheese, and cilantro.