Dissolve the salt in 4 quarts cold water in a large container. Add the beans and soak at room temperature for at least 8 hours or up to 24 hours, then drain and rinse well.

Adjust an oven rack to the lower-middle position and heat the oven to 250°F. Heat the oil in a Dutch oven over medium heat until it shimmers but does not smoke.

Stir in the onion, carrot, chard stems, and porcini mushrooms and cook until the vegetables are softened, about 7 to 10 minutes.

Stir in the white mushrooms and cover. Cook until the mushrooms have released their liquid, about 5 minutes, then uncover and continue to cook until the liquid has evaporated and the mushrooms are browned, 5 to 10 minutes.

Stir in the garlic and thyme and cook until fragrant. Add the broth, soaked beans, and bay leaves and bring the mixture to a boil.

Cover the pot and transfer it to the oven. Cook until the beans are almost tender, about 1 to 1 1/4 hours.

Stir in the chard leaves and tomato and continue to cook in the oven, covered, until the beans and vegetables are fully tender, 30 to 40 minutes.

Remove the pot from the oven and discard the bay leaves. Season with salt and pepper to taste and serve hot.