Put a cast iron skillet on the stove and brush it with olive oil. Once it gets very hot, place the mullet on the skillet and let them cook for about 10 minutes on each side.
Prepare the Emulsion: in a bowl add the lemon juice and the salt. Whisk the lemon juice until the salt has completely melted.
Add the olive oil and whisk again until you have a cloudy emulsion.
Add the parsley and pepper, mix and use immediately. If after a while the liquids separate, whisk them again