For the fish: Place an oven rack in the center of the oven. Preheat the oven to 450 degrees F. Spray a small baking sheet or glass baking dish with vegetable oil cooking spray. Set aside.
Season the halibut on both sides with the salt and pepper. Place on the baking sheet and drizzle with oil. Bake until the fish is cooked through and the flesh flakes easily with a fork, 10 to 15 minutes. Set aside to cool completely, about 20 minutes.
For the bread: Preheat a grill pan or a large nonstick skillet over medium-high heat. Remove some of the dough from the top half of the bread. Brush the cut-sides of the bread with olive oil. Grill the bread until golden, 1 to 2 minutes, and rub the cooked surface with the cut side of the garlic.
For the filling: In a medium bowl, combine the mayonnaise, sun-dried tomatoes, basil, parsley, capers, lemon zest, salt, and pepper.
Using a fork, flake the cooked fish and add to the filling. Mix until incorporated. Place the filling on the bottom half of the bread. Top with arugula. Add the top half of the bread and cut into 4 equal-sized sandwiches.