Preheat the oven to 350°F.
Melt the butter and set aside to cool.
Plan mold pan into freezer while you make the batter
Whisk the sugar and eggs in a large bowl until pale and foamy.
Add the flour and baking soda to the batter, whisking to combine.
Add the lemon zest, vanilla extract, and the cooled melted butter.
Stir everything to mix; batter will be thick.
Chill the batter for about 15 minutes in the fridge.
Brush softened butter onto a madeleine pan and lightly flour, knocking off excess.
Put a small cookie scoop worth of batter into the center of each mold (about 1 tablespoon). Do not spread or tap pan to even out!
Bake the madeleines for about 9 to 10 minutes, until they're golden along the edges and spongy to the touch.
Turn the madeleines out onto a wire rack to cool completely.