Special equipment: Three 12-inch metal or wooden skewers. If using wooden, soak in water for 30 minutes.
Preheat a grill or grill pan to medium heat.
Thread the carrots, onions, peppers, sweet potatoes and yams onto skewers, alternating vegetables. Brush the vegetables with olive oil and sprinkle with salt. Brush the ears of corn with olive oil and sprinkle them with salt. Place the skewers and corn on the grill and cook, turning every 2 or 3 minutes, until tender and slightly charred, 10 to 12 minutes. Remove the corn and skewers from the grill and let cool for 5 minutes. Cut the kernels from the corn cobs and remove the grilled vegetables from the skewers. Combine the corn and vegetables in a bowl and set aside.
Heat a large Dutch oven over medium heat. Add the 3 tablespoons olive oil, as well as the garlic, cumin, paprika, coriander and bay leaves and cook for 1 minute. Add the canned and fresh tomatoes and bring to a simmer. Add the black and red beans and the reserved corn and grilled veggies. Season with salt and pepper, cover and simmer over low heat for about 12 minutes.
Serve with the cheddar, sour cream and scallions.