Preheat your oven to 375°F (190°C).
Whisk together melted butter and flour, then use a pastry brush to lightly but thoroughly grease each cavity of your madeleine pan.
Set it aside.
In a small heatproof bowl, melt the remaining butter and let it cool.
In a large mixing bowl, combine the eggs, granulated sugar, light brown sugar, vanilla extract, and salt.
Whisk vigorously until fully combined.
Sift in the flour one-third at a time, gently stirring it into the egg mixture after each addition.
Drizzle the cooled melted butter around the edge of the batter (add lemon or orange zest if using)
Gently fold the butter and zest into the batter with a spatula until everything is well combined, being careful not to over-mix.
Drop the batter into the prepared pan by heaping spoonfuls.
Place the pan on the center rack of the preheated oven and bake for about 9 minutes, until the madeleines are light golden and spring back when lightly touched.
Immediately transfer them to a cooling rack.
Optionally, dust the cooled madeleines with powdered sugar or dip them in melted chocolate before serving.