Pan Fried Lemon Sole Meunière with Green Olive Sauce

Heat a large skillet (stainless steel preferred) over medium-high heat, until it passes the water droplet test (see notes).
While waiting for the pan to heat, pat the fish filet dry with a paper towel. Add flour to a plate or sheet pan. Season the filet with kosher salt and cracked black pepper, then dredge the filet in the flour on both sides. Lift the fish and gently shake off any excess flour.
Once the pan in pre-heated, add the oil or clarified butter over medium heat. Place the flour-dredged filet into the hot oil and cook until lightly browned, about 2-3 minutes, then carefully flip the fish and repeat for 2-3 more minutes. Remove fish from the pan and set aside.
Once the fish is removed, add the olive brine to the still-hot pan. Use the brine to deglaze the pan, using a wooden spoon or spatula to scrape up any browned bits on the bottom of the pan. Over medium-low heat, add the lemon juice and stir to combine, then simmer for 1-2 minutes. Add the chopped castelvetrano olives and stir.
Turn the heat off, then add the butter to the sauce and stir immediately to emulsify into the sauce. Continue stirring until the piece of butter is no longer visible.
Place the cooked sole filet on a serving plate. Use a large spoon to spoon the olive butter sauce onto and around the filet. Garnish with fresh chopped chives or parsley. Place the lemon zest strips on the top for extra garnish.