Preheat the oven to 350 degrees. Lightly oil a small loaf tin. Beat the egg whites until stiff and gradually add the sugar and vanilla; continue beating until all is incorporated.
Fold in flour and almonds. Bake for 50 to 60 minutes. Cool, wrap in foil and allow standing for 3 to 4 days. Slice the loaf very thinly with an electric knife. Place the slices on a baking tray and dry out in an oven preheated to 300 degrees for 30 minutes.