Turkey Andouille Chili

Name: Turkey Andouille Chili
Ingredients: 2 tablespoons peanut, canola, or vegetable oil, divided; 1 pound andouille sausages (4 links), chopped; 1 medium yellow onion, diced; 1 medium carrot, diced; Salt to taste; 2 jalapeno peppers OR 1 serrano pepper, seeded and minced; 1 poblano (pasilla) pepper, seeded and diced; 4-6 garlic cloves, minced; 2 teaspoons ground cumin; 2 teaspoons chili powder; 1 teaspoon paprika (regular or smoked); 1/4 teaspoon ground cinnamon; 1 pound ground turkey (preferably dark meat); 2 (14 oz) cans fire-roasted diced tomatoes; 2 (14 oz) cans low-sodium black beans; 1 (14 oz) can low-sodium pinto beans; 1 (14 oz) can low-sodium red kidney beans; Shredded cheddar or pepper jack cheese for serving (optional)