1. Place the beans in a colander and rinse with cold water. Pick over the beans to remove any stones. Place the beans in a clean pot, cover with fresh cold water and soak for at least 4 hours or overnight. Drain.
2. In a large pot, combine the beans, onion quarters, bay leaves, 1 1/2 teaspoons freshly ground black pepper, cumin, coriander and cayenne pepper with 3 quarts of water and bring to a boil.
3. Reduce heat and simmer until the beans are tender, about 1 hour.
4. Drain the liquid from the beans and remove the onions, garlic and bay leaves.
5. Combine the black beans, red onions, green and red peppers and corn in a large bowl. In a separate bowl mix the lime juice, vinegar, olive oil and salt. Pour over the beans and vegetables and toss to combine.
For the polenta:
1. Heat the olive oil in a pot over low heat. Add the garlic and cook for 1 minute, keeping the heat low so the garlic doesn't burn.
2. Add the milk, bay leaf and cayenne pepper. Increase the heat and bring the milk to a boil.
3. Pour the cornmeal into the hot milk slowly, whisking constantly. After all the cornmeal has been added, cook 3 to 4 minutes more, stirring constantly.
4. Remove the pot from the heat and slowly stir in the grated cheese. Season with salt and pepper to taste.
5. Place the polenta in warm bowls and top with the black bean salad.