Melt the butter on the stove on medium heat or microwave for 30 seconds, and let it cool at room temperature.
Mix room-temperature eggs, granulated sugar, vanilla extract, and freshly grated lemon zest into a medium bowl using a whisk.
Sift all-purpose flour, baking powder, and salt in a separate bowl.
Add the dry ingredients to the egg mixture and whisk until no streaks of flour remain.
Add melted butter to the mix(butter should be at a temperature of 120°F/50°C to avoid cooking the eggs) and whisk until combined.
Pour the mix into a bowl and cover with plastic wrap. Let the batter rest in the fridge overnight or, better, for 24 hours.
Next day, preheat the oven to 425°F/220°C, brush the madeleine mold with melted butter, and lightly dust in with the flour.
Take the batter from the fridge and put it into a pastry bag. Fill each mold cavity until 2/3 and place it into the oven middle rack.
Bake the madeleine for 3 minutes, then turn the oven off and bake another 8 minutes.Turn the oven back on to 320°F/160C and bake another 3/4 minutes or until the madeleines are perfectly golden brown.
Place the tray on a wire rack and remove the madeleines using a small offset spatula. Dust it with powdered sugar and serve still warm.