Preheat oven to 325°F. Grease a 8X8 inch baking pan.
Separate the egg whites from the yolks.
In a bowl, beat the egg yolks with the sugar until light. Add the butter and vanilla and continue beating for another minute or two. Add the flour and mix until fully incorporated. Slowly add the milk to the flour mixture and beat until everything is well mixed. Set aside.
In a separate bowl, beat the egg whites until stiff. Add the egg whites to the batter, a third at a time, gently whisking it until there are no more big white lumps (little ones are ok), repeat until all egg whites has been whisked in.
Pour the batter into the baking pan and bake for 40-60 minutes or until the top is golden brown. The baking time may vary depending on the oven, so check on the cake around 40 minutes and see how it looks.
Let the cake cool for at least 3 hours (preferably overnight in the fridge) before dusting it with powdered sugar and slicing.