Make a bed of herbs in a medium gratin dish or baking dish with the thyme, 4 of the parsley sprigs, and the bay leaves. Scatter the garlic on top. Season both sides of the fish with salt and pepper and place on top of the herbs. Add the vermouth and drizzle 2 tablespoons of the oil over the fish. Cover loosely with foil and bake until the fish is opaque, about 15 to 20 minutes, depending on how thick the fillets are.
Carefully pour the pan juices into a small saucepan and set the fish aside. Reserve the garlic and 4 thyme sprigs. Bring the sauce to a boil over high heat and cook until reduced by half, about 5 minutes. Whisk in the remaining 2 tablespoons olive oil and the lemon juice. Season with salt and pepper. Set aside.
Divide fish among 4 serving plates. Pour sauce over fish and garnish with the 4 remaining parsley sprigs, the reserved garlic and thyme, and tomatoes.