Preheat oven to 190°C. Take a 3 inch madeleine mold that has 12 cups, butter and flour this baking dish. Keep it aside.
Take a large bowl, add in the eggs and sugar, blend this mixture using a electric hand mixer. Then add in the vanilla extract, lemon zest, salt and continue blending.
Next, add in the flour and beat well to combine these ingredients together. Carefully add in the melted butter and continue blending. Then gently spoon a tablespoon of this batter each into the cups of the greased baking dish.
Bake these madeleines for 15 minutes till they swell and turn brown in colour. Once cooked, let them cool for 7-8 minutes and remove them from the baking dish.
Sprinkle the powdered sugar on top of these butter cakes and serve warm.