Preheat oven to 375 degrees F. Grease and flour two 12 (3-inch) madeleine pans. Set aside. (If you only have one, you can bake the cookies off in batches, just regrease and reflour after each batch).

Melt the butter in a medium saucepan, over medium heat until the crackling stops and brown bits form at the bottom. Immediately remove from the heat and pour out into a small dish, scraping up all those bits from the bottom. Set aside to cool to room temperature.

In the bowl of your stand mixer, fitted with the paddle attachment, beat the eggs, vanilla and salt, at high speed until light and fluffy, about 8 minutes. While the machine is running, slowly pour in the sugar in a slow and steady stream. Continue to be until the mixture is pale and very thick, 5 to 10 minutes.

Add the flour into the mixture in thirds, gently folding the flour in after each addition. Make sure not to over-mix the batter at this point or you'll end up with dry madeleines.

Stir in the orange zest, fresh orange juice and browned butter, make sure to gently fold it in, as quick as possible. Spoon the batter into the molds and give the pans a gently rap on the counter to dislodge any air bubbles. Bake until golden brown around the edges and the cookies spring back when you touch them, about 12 to 14 minutes. Remove from the oven and let them cool in the pans for about 5 minutes. Use a pairing knife to loosen from the pan and then invert onto a wire rack.

Dip the warm cookies in melted chocolate, or dust with powdered sugar. These cookies are best eaten the day of, but if you have leftovers, you can store them in an airtight container at room temperature for up to two days. Just keep in mind that they'll dry out slightly, but still be good for dipping in coffee or hot cocoa!