Brown the turkey: Heat olive oil in a large skillet over medium-high heat.
Add ground turkey, season with a pinch of salt and pepper, and cook until no longer pink, breaking it into crumbles. Don’t worry about crisping; light browning is enough.
Soften aromatics: Add diced onion and bell pepper to the pan. Cook 3–4 minutes until slightly softened.
Stir in garlic and cook 30 seconds until fragrant.
Bloom the tomato paste and spices: Push the mixture to one side. Add tomato paste to the cleared spot and cook 1 minute, then sprinkle in chili powder, cumin, smoked paprika, and coriander. Stir everything together to coat and lightly toast the spices.
Transfer to slow cooker: Move the turkey mixture to the slow cooker.
Add crushed tomatoes, diced tomatoes with chiles, kidney beans, black beans, and 1 cup of broth. Stir in cocoa powder and brown sugar. Season with 1–1½ teaspoons salt and ½ teaspoon pepper to start.
Set and cook: Cover and cook on Low for 6–8 hours or High for 3–4 hours.
Add more broth if you want a looser chili.
Finish and adjust: About 15 minutes before serving, squeeze in the juice of half a lime. Taste and adjust salt, pepper, and heat with cayenne or red pepper flakes. If it’s too acidic, add another ½ teaspoon of brown sugar.
If it’s too thick, splash in more broth.
Serve with toppings: Ladle into bowls and top with shredded cheese, a dollop of sour cream or yogurt, chopped cilantro, sliced jalapeños, or avocado. Serve with tortilla chips, cornbread, or over rice.