Step 1: Position a rack in the upper third of the oven; preheat to 450 degrees F.
Step 2: Cut the halibut into 4 pieces; arrange on a foil-lined baking sheet, cut-side down.
Step 3: Squeeze 1 lemon half over the fish and season with salt and pepper.
Step 4: Spread the mayonnaise over the tops.
Step 5: Bake until the fish is almost cooked through, 6 to 7 minutes. Switch the oven to broil.
Step 6: Broil the fish until the tops are golden, about 3 minutes.
Step 7: Meanwhile, combine the chives, dill and parsley in a small bowl; set aside.
Step 8: Toss the arugula with the juice of the remaining lemon half and 1 tablespoon olive oil; season with salt and pepper.
Step 9: Top each fish fillet with the herb mixture.
Step 10: Drizzle the arugula salad and tomatoes with the remaining 1 tablespoon olive oil; season with salt and pepper.
Step 11: Serve with lemon wedges.
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