Brush molds of a Madeleine pan with extra butter. Set aside. (I'm not sure, but i suspect if you don't have a Madeleine pan, you can use a mini muffin pan)
Melt 1/4 cup butter in a small saucepan over low heat. Remove from heat, and stir in honey and vanilla. Let cool 10 minutes.
Whisk flour, baking powder, cardamom, and salt in a small bowl; set aside.
Preheat oven to 325, with rack in center. Stir together sugar and eggs in a medium bowl. Gently fold in flour mixture until combined. Add butter mixture, and fold until combined. Cover with plastic wrap and refrigerate 30 minutes.
Spoon batter into prepared pan, filling each mold halfway. Tap pan on work surface to eliminate air bubbles. make until cookies are puffed and edges are golden, 7 to 8 minutes. Transfer pan to a wire rack; let cool slightly. Unmold cookies onto rack, and let cool completely.
Stir together sugar and orange zest and juice in a small bowl until glaze is smooth, thick, and opaque. Using a small pastry brush, coat ridges size of each cookie with glaze. Let stand 15 minutes.