In a large skillet/frying pan, melt half (1 teaspoon) of the butter. Add apples, cinnamon and brown sugar. Saute until tender -- stirring often. Empty contents to a bowl or plate and set aside
Clean the frying pan. Melt remaining butter. Pour in egg mixture. Cook as you would an ordinary omelet. When eggs are 90 percent set, flip the omelet. In the center of the open-face omelet, spread the sour cream and top that with most of the apple mixture.
Fold omelet and transfer to a plate. Top with remaining apple mixture.