In a 3-quart baking dish, combine the beans with 2 cups of water. Cover with plastic wrap and microwave on high for 15 minutes. Remove from the oven, carefully peel back an edge of the plastic, and let sit 5 minutes. Add 2 cups of very hot water, stir, recover, and let sit for 1 hour.
Drain the beans in a colander.
Heat the vegetable oil in the baking dish for 1 minute on high. Add the onions, garlic, jalapeno, bay leaf, chili powder, cumin, and salt, and stir to coat. Cook, uncovered, on high for 4 minutes. Stir well. Add the beans and stir to combine. Add 4 cups of hot water, stir, and cover tightly with plastic wrap. Cook on high for 30 minutes. Remove from the oven and let stand covered for 15 minutes. Carefully uncover and add the lime juice and cilantro. Stir well, and serve the chili topped with the avocado, tomato, and cheese