Brush the molds of a madeleine pan with butter and set aside.
In a small saucepan, melt the butter over low heat. Remove the pan from heat and stir in the honey and vanilla. Let cool about 10 minutes.
In a small bowl, whisk the flour, baking powder, cardamom, and salt; set aside.
In a medium bowl, stir together the sugar and eggs. Add in the flour mixture and stir until combined. Add the butter mixture and stir gently until butter is completely incorporated. Cover the bowl with plastic wrap and refrigerate at least 30 minutes.
Preheat oven to 325 degrees (F), setting the rack in the middle, while the batter is chilling.
Spoon the batter into the madeleine pan, filling each mold halfway. If necessary, use moistened fingers to press the batter into the mold.
Bake the cookies 7 - 8 minutes. They will have puffed up and the edges will become golden.
Remove the pan from the oven and let the cookies cool slightly. Unmold the cookies onto a wire rack and let them cool completely. This is very important.
In a small bowl, stir together the sugar, orange zest, and juice until the glaze is smooth and thick. Using a pastry brush, coat the ridged side of each cookie with the glaze. Let set 15 minutes.
To make these gluten-free, substitute sweet rice flour (or your favorite gluten-free flour blend) for the all-purpose flour; substitute vanillin for the pure vanilla; add 1/4 teaspoon xanthan gum to the dry ingredients.
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