Heat the olive oil in a large Dutch oven or heavy pot over medium heat. Add the diced onion and bell pepper, and cook for 4 to 5 minutes until softened.

Stir in the minced garlic and cook for about 30 seconds, until fragrant.

Add the ground turkey and cook, breaking it up with a spoon, until browned and cooked through, about 6 to 8 minutes.

Stir in the tomato paste, chili powder, cumin, smoked paprika, oregano, salt, black pepper, and cayenne if using. Cook for 1 minute to bloom the spices.

Add the kidney beans, black beans, crushed tomatoes, diced tomatoes, chicken broth, and brown sugar if using. Stir well to combine.

Bring the chili to a gentle simmer, then reduce the heat to low. Cook uncovered for 25 to 30 minutes, stirring occasionally, until thickened.

Stir in the lime juice and taste. Adjust seasoning as needed.

Serve hot with optional toppings like sour cream, avocado, chopped herbs, tortilla chips, shredded cheese, or sliced jalapeños.