Combine flour with salt and pepper on a large shallow plate.
Pat the sole dry with a paper towel and then sprinkle with coarse sea salt on one side.
Heat up 3 tablespoons of unsalted clarified butter in a sauce pan over medium heat.
Dredge fillets in the flour mixture until both sides are covered in the flour mixture. Shake off any excess.
Place the fillets in the saucepan with the hot butter.
Cook for 2-3 minutes on the first side until lightly brown.
Flip onto the second side and sprinkle fillets with zest and lemon juice. Cook for 2-3 minutes.
Remove the fillets from the pan and place on serving dish.
Keep the skillet on the stovetop and the heat to simmer (low-medium). Add the chicken stock, capers and 1 tablespoon of lemon juice. Bring to a simmer and stir throughout, scraping the fish renderings left behind in the pan into the sauce for more flavor. At this time, you may add some white wine (about 2-3 tablespoons). Cook for about 3-5 minutes until the sauce has reduced by a 1/3. Remove from heat, add 1 tablespoon of butter, stir until incorporated. Pour over the fish.
Serve immediately or cover with tin foil until remaining dishes for your menu are complete.
Garnish with chopped Italian parsley and/or slices of lemon.