Preheat the broiler.
Drain the beans and place in a pot with fresh cold water and the bay leaves. Bring to a boil, reduce heat and simmer the beans for about 1 ½ hours, or until tender. Skim the foam off the top as it forms. Drain the cooked beans well and set aside, covered.
While the beans are simmering, prepare the garlic and vegetables. Keep the half garlic head intact and cut off the tips of the cloves using a chef’s knife. Wrap the half garlic head in aluminum foil.
Cut the fennel bulb in half and then cut each half into 3 – 5 wedges, depending on the size of the bulb.
Toss the fennel and quartered onions with 3 – 4 tablespoons olive oil, 2 tablespoons balsamic and a little salt and pepper. Place on a shallow baking pan and at about 8 inches from the heat source. Place the garlic in a small baking tray and place it in the oven on the rack under the vegetables. Roast and broil respectively until the garlic is tender and the vegetables are nicely charred and tender. Turn them occasionally so that they cook and char on all sides. Remove and set aside.
If you have a stovetop smoker, place the herbal tea sprogs, rosemary and wood chips on the bottom and place the flat tray of the smoker over them. Place the drained giant beans on a small, shallow dish and place the dish on the rack, inside the smoker. Cover with the smoker’s sliding lid and smoke on top of the stove for about 10 – 12 minutes, or until the desired smoky flavor is reached. If you don’t have a home smoker, no problem! Place the herbs and wood chips on the bottom of heavy metal pan/ Place a piece of aluminum foil over them and a rack inside the pan. Place the giant beans on a small baking dish on the rack and cover the pan with aluminum foil, sealing the edges well. Place over one of your hobs on the stovetop and heat over medium flame, as with the home smoker, for 10 – 12 minutes, so that the beans acquire a deep, rich, smoky flavor. Remove from the smoker and set aside.
While the beans smoke, coarsely chop the sun-dried tomatoes.
Place the beans in a mixing bowl. Remove the foil from the garlic and squeeze out the soft cloves. Mash with the flat side of a knife and add to the beans, together with the charred vegetables, chopped sun-dried tomatoes, parsley, remaining olive oil, vinegar, salt and pepper and serve.