This section is from the book "Fruits And Their Cookery", by Harriet S. Nelson. Also available from Amazon: Fruits and Their Cookery.
Peel four not overripe bananas, cut them into round slices (not too thin), melt one ounce of butter in an omelet pan. When hot, put the bananas in and stir them in the butter for a few minutes, then season with salt and pepper. Break four eggs into a basin, add one tablespoonful of milk, salt and pepper to taste, and beat well. Melt one ounce of butter in an omelet pan, pour in the egg mixture, and stir over a quick fire until the eggs begin to set, then shape into an omelet. Put the prepared banana in the center, fold in the sides of the omelet and let it take color; then turn out into a hot dish and serve.
Proceed the same as directed in the foregoing recipe, but omit salt and pepper, and sweeten with sugar instead. When the omelet is ready to serve dredge the top with icing sugar and glaze the surface by placing it in a very hot oven for a few minutes.