Preheat the oven to 200 degrees.
Have 2 heat-proof dinner plates ready.
Combine the flour, 2 teaspoons salt, and 1 teaspoon pepper in a large shallow plate.
Pat the sole fillets dry with paper towels and sprinkle one side with salt.
Heat 3 tablespoons of the butter in a large (12-inch) sauté pan over medium heat until it starts to brown.
Dredge 2 sole fillets in the seasoned flour on both sides and place them in the hot butter.
Lower the heat to medium-low and cook for 2 minutes.
Turn carefully with a metal spatula and cook for 2 minutes on the other side.
While the second side cooks, add ½ teaspoon of lemon zest and 3 tablespoons of lemon juice to the pan.
Carefully put the fish fillets on the ovenproof plates and pour the sauce over them.
Keep the cooked fillets warm in the oven while you repeat the process with the remaining 2 fillets.
When they’re done, add the cooked fillets to the plates in the oven.
Sprinkle with the parsley, salt, and pepper and serve immediately.