Preheat the oven to 400 degrees F.
To brown the butter, melt the butter over medium heat in a heavy saucepan, allowing to bubble and foam, stirring frequently. Once the foaming subsides, allow the butter to brown along the bottom and then remove the pan from the heat. Browning will take about 5 minutes total; do not burn.
In a medium bowl, mix the eggs, sugar, and honey with electric mixer until thick and pale. Add the browned butter and mix.
In a small bowl, sift together the flour, baking powder and 1/4 teaspoon salt, and mix into liquid ingredients, along with zest, just until blended.
Fill the greased madeleine baking molds and bake until golden, 9 to 11 minutes.
*Cook's Note: you may substitute a mini-muffin pan for madeleine molds.