Heat olive oil in a large soup pot over medium heat. Add turkey; cook, stirring often, until crumbly, browned, and no longer pink, about 10 minutes. Drain and discard any fat.

Transfer turkey to a slow cooker; stir in diced tomatoes, pumpkin, chili beans, black beans, onion, brown sugar, pumpkin pie spice, and chili powder. Cover slow cooker.

Cook on Low until pumpkin is tender and starts to break apart, at least 3 hours.