Dissolve the salt in 4 quarts of cold water in a large bowl. Add the bean mix and soak at room temperature for at least 8 hours or up to 24 hours. Drain and rinse the beans thoroughly.

Adjust an oven rack to the lower-middle position and heat the oven to 250 degrees.

Heat the oil in a large Dutch oven over medium heat until shimmering. Add the onion, carrot, chard stems, and porcini mushrooms. Cook until the vegetables are softened and the onions are translucent, about 5 to 7 minutes.

Add the white mushrooms and increase the heat to medium-high. Cook, stirring occasionally, until the mushrooms have released their liquid and are beginning to brown, about 8 to 10 minutes.

Stir in the garlic and thyme and cook until fragrant.

Stir in the vegetable broth, bay leaves, and the soaked beans. Bring the mixture to a simmer over high heat.

Cover the pot and transfer it to the oven. Bake until the beans are completely tender, 1.5 to 2 hours. Taste several different types of beans from the mix to ensure even doneness throughout.

Remove the pot from the oven and discard the bay leaves. Stir in the chard leaves and tomato, cover, and let the soup stand until the chard has wilted, about 5 minutes. Season with salt and pepper to taste and serve hot.