Grease your madeleine pan really well with butter. If you want extra insurance, dust it lightly with flour and tap out the extra.

In a bowl, whisk the eggs and sugar until it looks lighter and a bit foamy, about 1 to 2 minutes by hand. You do not need a mixer, but you can use one if you want.

Whisk in vanilla and lemon zest.

In a separate bowl, mix flour, baking powder, and salt.

Add the dry ingredients into the egg mixture and stir gently just until you do not see dry flour.

Pour in the melted butter and fold until the batter looks smooth and shiny.

Cover the bowl and refrigerate the batter for at least 45 minutes, or up to overnight.

Preheat your oven to 375°F (190°C).

Spoon batter into the shells, just a heaping teaspoon or so per cavity, depending on your pan size.

Bake 9 to 11 minutes, until the edges are golden and the tops spring back when lightly touched.

Tap the pan gently to release, then move them to a rack. Dust with powdered sugar if you like.