Preheat oven to 350 degrees. Brush an 8-inch round cake pan with oil. Place a round of waxed or parchment paper in the bottom; brush with oil, and dust with flour, tapping out excess. Set aside.
In a medium bowl, whisk flour, baking soda, cardamom, and salt; set aside. In a small bowl, whisk eggs, sugars, yogurt, and oil until smooth. Gently mix egg mixture into dry ingredients until moistened; mix in carrots. Transfer batter to prepared pan.
Bake until a toothpick inserted in center comes out clean, 40 to 45 minutes (if browning too quickly, tent cake with aluminum foil). Cool in pan, 15 minutes. Turn out of pan, remove paper, and cool completely on a rack, right side up. Apply glaze, or dust with confectioners’ sugar.