Preheat oven as high as it goes, 500°F.
Season the fish inside and out with salt and pepper, and drizzle with olive oil. Fill each fish cavity with fennel seed, 2 cloves crushed garlic, a few sprigs each of the herbs plus a bay leaf and lemon slices.
Add olive oil to a roasting pan and add the tomatoes, a few sprigs of thyme, remaining garlic cloves, shallots, salt, pepper and vermouth. Toss and arrange fish on top of the tomatoes. Place lemon halves in pan cut-side down and roast fish until flaky and opaque, and the skin is crispy, 15-18 minutes. When you remove the pan from the oven, douse the fish with the juice of the halved, roasted lemons.
For the slaw, toss parsley, fennel and celery with lemon juice and EVOO, and season with flaky sea salt.
To serve, lift the fish filets away from bones carefully with a serving fork and serving spoon. Serve a full filet of crispy-skin branzino on a bed of roasted tomatoes and sprinkle fennel-celery slaw down the length of the filet.