In a large dutch oven, heat 2 tablespoons olive oil over high heat. Working in batches, add the ground turkey and cook, breaking up the meat, until browned; transfer to a bowl.
Lower the heat to medium-high and add the remaining 1 tablespoon olive oil to the pot. Add the bell peppers, onion and garlic and cook, stirring occasionally, until crisp-tender, about 5 minutes. Stir in the oregano, chili powder, cumin and 2 teaspoons salt and cook until the vegetables are softened, about 3 minutes. Add the tomatoes, black beans, wine and bay leaves. Stir in the turkey and 1 cup water, lower the heat to medium and simmer until thickened, about 1 hour and 45 minutes. To serve, top with the cheddar cheese.