In a small sauce pan combine the garlic, anchovy, and olive oil over medium low heat and cook until the anchovy is melted and the garlic is soft, about 4 minutes
Heat the grill to medium high heat
Grill the lemon cut side down until charred then set aside
Dress the broccolini and mushrooms in olive oil with big pinches of salt and black pepper
Grill until cooked through and a little charred then remove from the grill
Liberally coat the fish with oil and season with salt and pepper
Grill the fish, skin side down, until cooked through and the skin is blistered
Transfer the fish to serving plates alongside the broccolini and mushrooms then spoon the anchovy mixture all over and serve with one of the grilled lemon halves to squeeze over the whole thing