Season the halibut with the Old Bay or salt and pepper and drizzle with EVOO. Using a food processor, pulse the basil, parsley, dill, capers, shallot, garlic and anchovies with 1/3 cup EVOO until finely chopped.
In a large skillet, cook the halibut, turning once, over medium-high heat until cooked through, about 7 minutes. Top the fish with the green sauce.
Dress the arugula with the lemon juice, a drizzle of EVOO and salt. Serve the greens with the fish and bread.