Dice onion, bell pepper, and mince garlic. Drain and rinse both cans of beans.
Heat olive oil in a Dutch oven over medium-high heat. Add ground turkey and brown for 6-8 minutes, breaking it apart.
Add onion and bell pepper, cook for 4-5 minutes until softened. Add garlic and cook for 1 minute until fragrant.
Add chili powder, cumin, smoked paprika, salt, and pepper. Stir and cook for 1-2 minutes to bloom the spices.
Add crushed tomatoes, chicken broth, kidney beans, and black beans. Stir to combine.
Bring to a boil, then reduce heat to low. Simmer uncovered for 30-35 minutes, stirring occasionally.
Preheat oven to 400°F (200°C). Grease a 9x9 baking pan or cast iron skillet.
In a large bowl, whisk cornmeal, flour, sugar, baking powder, and salt.
In a medium bowl, whisk buttermilk, vegetable oil, and eggs until smooth.
Pour wet ingredients into dry ingredients. Stir until just combined; do not overmix.
Pour batter into prepared pan. Bake for 20-22 minutes until golden and toothpick comes out clean.
Taste chili and adjust seasoning. Serve hot with a square of cornbread and desired toppings.