Beat the eggs: Crack the eggs into a bowl, and whisk with sugar until the mixture becomes light and fluffy.
Add other ingredients: Add flour, milk, and vanilla extract to the egg mixture and stir well. Melt the butter and add it to the mixture. If you want a fluffier cake, add baking powder and mix well.
Bake the cake: Preheat the oven to 170°C (338°F). Pour the batter into a greased cake pan. Bake for about 25–30 minutes, and check with a toothpick (insert it into the cake, if it comes out clean, the cake is done).
Serve: Let the cake cool, then cut it into pieces.
Notes:
You can substitute butter with cooking oil if you prefer a lower-fat cake. This egg cake can be served with fresh fruit, cream, or chocolate sauce.