Pat the flounder fillets dry with paper towels.

Sprinkle salt and pepper on both sides of the fillets.

In a large skillet, heat the butter and olive oil over medium-high heat.

Once the oil is hot, carefully place the fillets in the skillet. Cook for about 3-4 minutes on each side until golden brown.

After flipping the fish, squeeze in the lemon juice and add the zest.

Check for doneness, the flounder is ready when it flakes easily with a fork, which usually takes about 8 minutes total.

Remove the flounder from the skillet and place it on a serving platter. Sprinkle with chopped parsley for garnish.

Serve the flounder warm with your favorite sides.