Pat the fish filets thoroughly dry with paper towels, then season generously on both sides “from above" with salt and pepper. Set aside.
Warm a cast iron skillet over medium-low heat, add the butter and allow to melt, and then turn light, golden brown, about 5 minutes.
Add both fish filets to the skillet, and allow them to cook, undisturbed for about 1 minute.
Next, add the rosemary and thyme, and give the pan a shake, incorporating them into the butter. Continue cooking, using a spoon to baste some of the now herb-infused butter over the top sides of the fish, about 2 minutes more.
Use a fish spatula to gently flip the fish, and continue cooking, and basting, 3 minutes more, or until the fish is cooked through.
To serve, spoon the mint, caper, and olive relish onto the bottom of a plate, and set the fish on top, followed by spoons of the herbed butter from the pan. Serve additional relish on the side.