Heat oven to 350ºF. In a medium saucepan over low heat, bring the olive oil to 300 to 310ºF on a digital instant-read thermometer.
While the oil is heating, season the flounder fillets on all sides with kosher salt and freshly ground black pepper. Lay half of the sliced lemons and half of the parsley in the bottom of a 12-inch cast-iron skillet. Lay the seasoned fillets on top of the lemons in a single layer without overlapping. Top with the remaining lemons and parsley. Once the oil has reached temperature, gently pour it over the fillets, place in the oven, and poach for 10 minutes. Allow to cool for 5 minutes before serving.
Flounder Fish Salad
Whisk together the oil and vinegar in a medium mixing bowl. Add the black pepper, salt, lime juice, hot sauce, scallions, parsley, and lemon, and stir to combine. Taste and adjust the seasoning, if desired. Add the fish and gently mix to combine.