Step 1

Pat rockfish fillets dry.  Dust with flour, and shake off any excess.  Sprinkle them on both sides with salt and pepper.Prepare a heavy pan with the olive oil and 1 TB butter. Heat on medium-high until butter is melted but not browned, then turn the heat down to medium.

Step 2

Place the fillets in the pan and cook about 3 minutes. Don't touch the fillets until they're ready to flip.Use a thin metal spatula to test the fish.  If you can slide the spatula under the fish without the fish sticking to the pan, it's ready to flip. If the fillets won't release, give them another 30 seconds. They'll release when they've finished cooking.After flipping, divide the remaining 1 TB butter over both fillets.

Step 3

Cook fish another 2-3 minutes until done. Fish will be golden on both the top and bottom and opaque all the way through when finished cooking.Transfer the fish to plates, leaving the excess butter in the pan. Cover fish to keep warm, or set fish in a 200ºF oven.Reduce heat to medium.  Add the lemon juice and capers, and stir with a wooden spoon. Add half the herbs and stir again. Serve fish hot with pan sauce and remaining herbs.