Thaw fish if necessary and blot dry with paper towels. Combine salt and pepper in a small bowl and sprinkle it on both sides of each fish fillet. Lightly dredge the fillets in flour, shaking or patting off the excess, and set the fish on a baking sheet or cutting board in a single layer.

Heat 2 tablespoons oil in a 12 inch non-stick skillet over medium high heat. Swirl the oil around the pan to coat the bottom as much as possible. Gently lay half the fillets in a single layer into the pan and let them cook (without moving them) for 2 to 3 minutes so the bottom can brown.

Flip each fillet over with two spatulas, one underneath and one to catch the topside when gently flipped over. This method helps keep the fish from falling apart. Cook for 1 minute on the other side, then remove the fish fillets to a clean plate or platter and tent with foil. Wipe out the skillet and repeat with the remaining fish fillets.

When the second batch of fish is done, do not wipe out the skillet. Add the butter and whisk constantly until the butter melts. Continue to whisk until the butter turns a slight brown and has a nutty smell/aroma, another 2 or 3 minutes. (The browning happens quickly, so keep a close eye on it.) Off heat, stir in the lemon juice and thyme. Season will a pinch of salt and pepper and pour over the fish fillets and serve.