In a large pot, heat the olive oil over medium heat. Add the diced onion and minced garlic and sauté until the onion becomes translucent, about 3-4 minutes.
Add the ground beef (or turkey) to the pot. Cook until browned and fully cooked, breaking it apart with a spoon as it cooks, about 5-7 minutes. Drain excess fat if necessary.
Stir in the black beans, kidney beans, diced tomatoes with green chilies, enchilada sauce, corn, chili powder, cumin, smoked paprika, and salt and pepper. Mix well to combine.
Bring the chili to a gentle simmer, then reduce the heat to low. Cover and let it cook for about 20 minutes, stirring occasionally.
Taste the chili and adjust seasonings if needed. Stir in 1 cup of shredded cheddar cheese until melted and well incorporated.
Serve hot, topped with the remaining shredded cheese and garnish with chopped cilantro and sour cream if desired.