Combine the beans, water, mushrooms, bay leaves, salt, and baking soda in a large saucepan. Bring to a boil over high heat, skimming any foam or impurities that rise to the surface. Cover, reduce the heat to low, and simmer gently until the beans are completely tender, about 1 1/4 to 1 1/2 hours. If the beans remain firm after 90 minutes, add another cup of water and continue simmering until soft. 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 for 12 to 15 minutes, stirring occasionally, until the vegetables are softened and just beginning to turn golden brown.

Stir in the garlic, cumin, and pepper flakes and cook until fragrant. Pour in the broth and the cooked beans with their cooking liquid and bring to a boil. Reduce the heat to medium-low and simmer uncovered for 30 minutes, stirring occasionally, to allow the flavors to meld.

Transfer 1 1/2 cups of the beans and 2 cups of the cooking liquid to a blender and process until completely smooth, about 1 minute, then return the puree to the pot. Whisk the cornstarch and water together in a small bowl, then gradually stir half of this mixture into the simmering soup. Continue to simmer for 3 to 5 minutes until slightly thickened; if you prefer a thicker consistency, add the remaining cornstarch mixture.

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