Place the beans in a large bowl. Sort through them and discard any stones or debris. Cover with 2 to 3 inches of water and discard any beans that float. Soak at room temperature for 8 hours or overnight. Drain and rinse well.
Place the beans in a large pot and cover with 2 inches of water. Bring to a boil. Reduce the heat and simmer, uncovered, for 30 minutes. Skim any foam off the top, then add the shallots, garlic, fennel, salt, lots of freshly ground black pepper, and the kombu, if using. Continue simmering until tender, up to 2 more hours, stirring occasionally. The timing will depend on the type and freshness of your beans (older beans will take longer than fresher beans). I typically check them every 30 minutes. Add more water to the pot, as needed, as it starts to evaporate.
When the beans are tender, remove the garlic, fennel stalks, and kombu. Discard the garlic papers. Use the back of a knife to mash the soft garlic cloves into a paste, then return it to the pot. Stir in the olive oil and lemon juice, and season to taste. I like to add 1/2 to 1 teaspoon more salt, more pepper, and a pinch of red pepper flakes.
Add the chard leaves and cook until the chard is just wilted. Season to taste and serve in bowls with drizzles of olive oil and crusty bread. Sprinkle with parsley.
*The kombu is optional, but it helps the beans become more digestible. Kombu can get bitter if boiled, so be sure to keep the beans cooking at a gentle simmer after you add it.