In a medium saucepan over low heat, bring the olive oil to 300 to 310 degrees F.
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 cast iron skillet large enough to hold the fillets in a single layer without overlapping. Lay the seasoned fillets on top of the lemons. Top with the remaining lemons and parsley. Once the oil has reached temperature, gently pour it over the fillets, and place in the oven and poach for 10 minutes. Allow to cool for 5 minutes before serving.