Coat a large pot with olive oil over medium-high heat.
Add the onion and bell pepper and sauté, stirring occasionally, until the onion softens.
Add the garlic, stir everything together, and cook until fragrant, about 30 seconds.
Add the ground turkey and use a spatula to break up the meat as it cooks.
Continue to cook about 6–7 minutes, until fully cooked.
Add pumpkin puree, diced tomatoes, tomato paste, broth, chili powder, cocoa powder, pumpkin pie spice, cumin, kosher salt, black pepper, and cayenne pepper (if desired). Stir together. Reduce heat and simmer for 20–30 minutes, stirring occasionally.
Transfer to a bowl and top with toppings such as avocado, arugula, a dollop of yogurt, pumpkin seeds, tortilla chips, or cheese!