How to Make It
Put the parsley, capers, garlic, lemon juice, anchovy paste, mustard, 1/4 teaspoon of the salt and 1/8 teaspoon pepper in a blender. Pulse to chop. With the machine running, add 7 tablespoons of the oil in a thin stream to make a smooth puree.
Put the potatoes in a medium saucepan of salted water. Bring to a boil, reduce the heat, and simmer until tender, about 15 minutes. Drain.
Light the grill or heat the broiler. Coat the fish with the remaining 1 tablespoon oil and sprinkle with the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Grill or broil the fish for 3 minutes. Turn and cook until just done, 3 to 4 minutes longer.
To serve, drizzle some of the salsa verde over the fish and potatoes. Serve the remaining salsa verde alongside.
Fish Alternatives In place of the catfish, you can use swordfish, salmon, halibut, or tuna steaks, or mahimahi or mackerel fillets—really almost any fish you can grill.