Soak beans in a large bowl of water to cover for several hours or overnight. Drain.
Place soaked beans into a pot with stock or broth and enough water to cover by 2 inches.
Add bay leaf and whole garlic cloves.
Heat to a boil, reduce heat to medium-low and simmer, covered, until beans are tender (about 45 minutes). (The beans should be softer than al dente but not cooked to the point where they begin to disintegrate.)
Don’t drain beans until fennel and tomato sauce is cooked.
Meanwhile, cut stalks off fennel bulb. Chop the feathery leaves and reserve. Trim off root end of the bulbs; cut bulbs in half lengthwise and slice thinly. There should be about 8 cups of fennel slices. Discard stalks or save for soup.
Heat 1/3 cup olive oil in a large heavy skillet; cook fennel over medium-low heat until wilted and translucent, about 10-12 minutes. Do this in batches if necessary.
Add tomato to fennel; cook 5 or 6 minutes.
Discard garlic and bay leaf from beans; drain beans. Add beans to the skillet, tossing gently to combine all the ingredients.
Add parsley and chopped fennel leaves. Season with salt and pepper.
Remove from heat, add lemon juice and remaining olive oil to taste.