Combine the beans, water, mushrooms, bay leaves, salt, and baking soda in a large saucepan. Bring to a boil, skimming off any foam that rises to the surface, then cover and reduce heat to low to simmer gently until the beans are tender, about 75 to 90 minutes. If the beans are still firm after this time, add an extra cup of water and continue simmering. Discard the bay leaves but do not drain the beans.

Heat the oil in a Dutch oven over medium heat until it shimmers. Add the onions, celery, and carrot and cook, stirring occasionally, until the vegetables are softened and lightly browned, about 12 to 15 minutes.

Stir in the garlic, cumin, and pepper flakes and cook until fragrant, about 1 minute. Pour in the vegetable broth and the cooked beans along with all their cooking liquid, bring to a boil, then reduce the heat to medium-low and simmer uncovered for 30 minutes to allow the flavors to meld.

Transfer a portion of the beans and liquid to a blender and puree until completely smooth, then return the mixture to the pot to thicken the base. Whisk the cornstarch and water together in a small bowl, then gradually stir half of the slurry into the simmering soup and cook for 3 to 5 minutes until slightly thickened; if you prefer a thicker consistency, add the remaining slurry and simmer for another minute.

Remove the pot from the heat and stir in the lime juice. Season with salt and pepper to taste and serve hot.