Melt the butter in a saucepan over a low-medium heat. Once melted, set aside to cool.
Beat the sugar and eggs together until the mixture is pale and thick, and holds the figure of 8 when the whisk is lifted out of the batter (approx. 5-8 minutes using a handheld electric whisk/stand mixer).
Add the vanilla extract and lemon zest and beat briefly until distributed evenly throughout the batter.
Sieve in half of the flour and the salt. Gently fold in using a spatula or wooden spoon until combined.
Fold in the remaining flour.
Add one ladle of batter into the melted butter and stir until completely combined. Then add this to the rest of the batter; stir until the batter has thickened and looks smooth and shiny.
Cover the batter and place in the fridge to chill for 40-45 minutes.
Preheat the oven to 180℃ and - using a pastry brush - grease the madeleine tin with 2 tbsp melted butter.
Spoon 1 heaped tbsp of the cooled batter into the centre of each scalloped shape in the tin. Cover excess batter and place in the fridge if you don't have two madeleine tins to bake all of the batter at the same time.
Bake for 10-12 minutes until risen and golden.
Turn the madeleines out of the tin while they are still warm. Transfer onto a wire rack to cool completely.