Rinse and pat your fish filets completely dry. Brush your fish with 1 tbs oil all over. Season with salt + pepper to taste.
Add the remainder olive oil to a pan and heat on HIGH. Once hot, add your fish skin side up. Lower heat to medium high and sear each side for a few minutes per side, until golden.
Transfer pan to your oven and bake for 10-15 minutes (time varies along with the thickness of your fish). Internal temperature should be 145 F.
Whisk together the melted butter and lemon juice. Pour over your fish, garnish with dill and freshly ground black pepper.