Preheat oven to 400 degrees F (200 degrees C). Grease a small baking dish.
Beat eggs, vegetable oil, and vanilla extract together in a large bowl. Mix barley flour, sugar, baking powder, and salt together in a separate bowl; add to eggs mixture and stir to make a smooth batter. Pour batter into prepared baking dish.
Bake in preheated oven until brown on top and set in the center, 20 to 30 minutes.
