Preheat oven to 325°F. Grease an 8"x8" baking dish lightly with butter.
Melt the butter and let it cool slightly. Warm the milk until lukewarm and set aside.
Whip egg whites with vinegar until they form stiff peaks. Set aside.
Beat egg yolks with confectioner's sugar until light and fluffy. Mix in melted butter and water until well combined, about 2 minutes.
Add flour and mix until fully incorporated. Gradually add lukewarm milk and vanilla extract, mixing until smooth.
Gently fold in whipped egg whites, one-third at a time, until fully incorporated.
Pour the batter into the prepared baking dish. Bake for 45-60 minutes, until the center is just slightly jiggly. If the top browns too quickly before 45 minutes, cover with aluminum foil for the remaining baking time.
Let the cake cool completely before slicing. Dust with additional confectioner's sugar. To speed up cooling, refrigerate the cake. The cake will remain slightly jiggly even after fully cooled, due to the custard layer.