How to Make It
Prepare the Cauliflower: Combine water, wine, brown sugar, salt, and bay leaves in a saucepan large enough to hold cauliflower; bring to a boil over high. Reduce heat to medium-low, and add cauliflower (stem side up). Cover and simmer until tender, about 20 minutes. Remove from heat. Drain and discard liquid. Pat cauliflower dry with paper towels.
Prepare a wood or charcoal grill with wood or charcoal on 1 side of grill (to create direct and indirect heat). Heat to high (450°F to 550°F). Add 2 handfuls of medium-size (about the size of a golf ball) cherry wood chunks to coals. Let stand until wood chunks start to smoke, 5 to 10 minutes. Place cauliflower on oiled grate over indirect heat. Coat cauliflower generously with olive oil cooking spray, being careful not to spray near open flame. Open vent holes on grill lid, and close grill lid, with vent holes above cauliflower. Smoke until golden brown, about 20 minutes, turning every 8 to 10 minutes. (Be careful not to break up the cauliflower; a spatula is your friend here.)
Prepare the Vinaigrette: Whisk together lemon juice, shallot, mustard, thyme, salt, and pepper in a small bowl; let stand 10 minutes. Whisk in oil.
To serve, break cauliflower into florets on a platter or present whole and carve it at the table; drizzle each serving with about 2 tablespoons of the vinaigrette. Sprinkle with pomegranate arils and parsley.