Season the fish on both sides lightly with salt and pepper and set aside while you prepare the skillet.
Add the oil into a large cast-iron skillet and tilt around to cover the bottom with the oil. Place onto medium-high heat. Once the pan is hot, place fish into the hot oil and allow to cook for about 3 to 5 minutes. Go ahead and very very gently shake the fish around in the skillet for a few seconds as it sears. Fish is notorious for sticking to a skillet and we don’t want that to happen. The fish is ready to turn when it releases easily from the skillet to turn over.
After turning the fish over, turn the heat down to medium and allow the fish to cook on the other side for about 3 to 5 minutes. Fish is done when it is golden brown and flakes easily with a fork. Transfer the fish to a plate covered with paper towels and set it aside.
Deglaze the hot skillet with the white wine while still on medium-high heat. Add the white wine slowly and gently scraping the bottom to release the browned bits.
Now add the butter and move it around with a fork until it is completely melted. Remove the skillet from the heat and add the lemon juice and zest. Return the skillet to the heat and add the thyme sprigs. Continue to cook for 1 or 2 minutes, or until heated completely through. Remove from heat and discard the thyme stems.
Note: Lemon juice will make the hot butter pop which is why we remove the skillet from the heat while adding.
Place the fish into the sauce in the skillet just long enough to coat each piece with the sauce. Place the rich sauce bathed fish onto individual serving plates and spoon some of the lemon-thyme butter sauce over each one.
Serve and enjoy!