Brush molds of a madeleine pan with butter; set aside. Make the batter: Melt 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 degrees, 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. Bake 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.
Make the orange glaze: 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 ridged side of each cookie with glaze. Let set 15 minutes. Cookies can be stored in a single layer in an airtight container up to 3 days.