Place butter, onion, and garlic in rice cooker; close lid and turn on cooker. Cook until onion is soft and translucent, stirring occasionally, 10 to 15 minutes. Add chicken broth, milk, polenta, and salt. Cover and cook on full cycle, stirring occasionally, until polenta has absorbed the liquid, about 20 minutes. Add Cheddar cheese, Parmesan cheese, and black pepper; stir until cheese is melted.