In the bowl of a stand mixer, combine eggs, granulated sugar, brown sugar, lemon zest and vanilla extract; process on medium-high speed for 5 minutes.
Meanwhile, in a small saucepan over medium-low heat, melt ½ cup butter. When melted, remove from the heat and set aside.
In a medium bowl, combine flour, rosemary, baking powder and salt; whisk for a few minutes and set aside.
After 5 minutes, stop the mixer and add the dry ingredients; process on low speed for 1 minute. Fold in the melted butter with a spatula until well incorporated. Cover the bowl with plastic wrap and transfer to the refrigerator for 30 minutes.
Preheat oven to 375ºF.
Brush the Madeleine molds with melted butter (2 tbsp.) using a pastry brush. Dust the cavities with flour, tilting the pan to coat evenly. Turn the pan upside down to remove any excess flour.
Half an hour later, stir the batter and divide it among the prepared molds, filling them about ¾ full.
Transfer to the preheated oven and bake for 9 to 12 minutes or until they spring back when gently touched and the tops are light golden brown.
Remove from the heat and allow to cool 2 minutes before placing the madeleines on a wire rack to cool for 10 minutes (pattern side up).
Using a fine sieve, lightly dust the tops with confectioners’ sugar if desired.