Place the eggs in a bowl of a stand mixer fitted with a whisk attachment. Whip on medium-high speed, adding the sugar a little at a time, until all the sugar is incorporated. Turn the mixer to high and whisk until the eggs have doubled in volume, 3 to 5 minutes.

Remove the bowl from the stand mixer and stir in the flour, baking powder, salt and vanilla extract. Cover the bowl and allow to rest for at least 30 minutes and up to an hour.

Meanwhile, melt the butter in a small saucepan over medium heat. (Remove and reserve 2 tablespoons of the butter for brushing the pans.) Add the honey and cook, stirring until smooth, about 1 minute more. Remove from the heat and allow to cool, about 30 minutes.

Stir the butter and honey mixture (rewarm to liquefy if necessary) into the batter until smooth. Cover the batter and allow to rest for an additional 30 minutes or up to an hour.

To make the madeleines, preheat oven to 400 degrees F. In madeleine molds, brush indentations with the remaining 2 tablespoons melted butter. Using a tablespoon (I use a little cookie scoop), fill each indentation in the molds three-quarters full with batter. Tap the pan on the counter to distribute the batter evenly (I found this step wasn’t necessary. The batter spread in the baking process.). Bake until deep golden brown, about 8 to 10 minutes. Remove from the oven, allow to cool for 30 seconds, and then tip them out onto a cooling rack.

Dust with powdered sugar and serve. Madeleines are best when served still warm but are delicious when cooled.