It is important to score the fish and and to season it before poaching. Scoring ensures that the olive oil will reach the innermost portion of the flesh. Seasoning will flavor the whole fish evenly. That is the smarter way rather than relying on the sauce alone which is added only after the fish is cooked.Use regular olive oil, not extra virgin which is too bitter.
Rinse the fish well then pat dry with a kitchen towel.
Score both sides of the fish and rub generously with salt and pepper.
In a wide shallow pan that can hold all the fish in a single layer, pour in enough olive oil to reach a depth of two inches.
Heat the oil to 160F to 180F (see notes after the recipe).
Lay the fish on the oil and cook for ten minutes per side.
Make the lemon butter sauce
In a small non-reactive pan, heat the white wine vinegar with the garlic very gently over low heat for about a minute. Leave to infuse for a few minutes. Strain.
Stir together the melted butter and strained white wine vinegar. Squeeze in the juice of half a lemon.
Season with salt and pepper. Taste. Adjust the amount of lemon juice, salt, pepper or all of them, if needed.
Assemble the dish
Lay the poached fish on a serving platter or individual plates.
Drizzle sauce over the enter firsh.
Arrange the olive slices on top of the fish.
Sprinkle with mint leaves.
Notes
Based on a recipe from the Italian cookbook, The Silver Spoon.