Wash the flounder fillets. Place in a dish and stir up with the sour cream. Let stand at least 5 minutes.
Dip the fillets in flour; shake off excess and place on rack to dry some.
Heat the olive oil and 1 tablespoon of butter in a frying pan large enough to hold fillets in a single layer. Brown lightly on both sides until cooked. Season with salt and pepper when the fillets are turned over.
Remove fillets and keep warm on a separate plate in the oven.
Add 1 tablespoon butter, parsley, and lemon juice; stir around, scraping up the browned bits. Turn off heat and let sit for 5 minutes.
Pour flavored butter over flounder fillets just before serving.
Beverly Pepper, The Glamour Magazine After Five Cookbook, 1952http://macheads2.net/recipes/FlounderMeuniere.html