Mash the anchovy with the garlic in a medium bowl. Then, whisk in the parsley, basil, chives, capers, lemon zest and juice, and olive oil. Season to taste with salt and pepper.
Brush the fish with a little high-heat oil and season with salt and pepper.
Heat 2 tablespoons of the ghee in a large oven-safe skillet over medium-high heat. Be sure the ghee coats the surface of the skillet.
When the ghee is hot and slightly smoking, add the fish, flesh side down. Let the fish cook for 3 to 4 minutes, until the bottom edges become golden brown. The fish will be ready to flip when it easily comes off the bottom of the pan. If it feels like it’s stuck, just let it sit for 30 seconds longer.
Flip the fish, remove from the heat, and transfer the skillet to the oven. Let the fish finish cooking in the oven for 4 to 5 minutes, or longer depending on its thickness. To check for doneness, take a fork and pierce the thickest part of the fillet. If it flakes easily or if it looks opaque, your fish is done. Fish will cook a bit longer once it is removed from the oven.
Remove the skillet from the oven and let the fish rest for 1 to 2 minutes. Place the fish fillets on a platter or individual plates and ladle with a little of the sauce verte. Serve immediately.