1. Preheat oven to 350°.
2. Spray a 9- x 3- x 5-inch loaf pan with cooking spray and dust with flour. Set aside. In a medium bowl, whisk together flour, baking powder, baking soda, cinnamon, and salt. In a separate bowl, whisk together sugar, 1/3 cup yogurt, oil, eggs, and ginger. Stir dry mixture into yogurt mixture, then stir in carrots. Transfer to baking pan.
3. Bake for 40 to 50 minutes, until a toothpick inserted in the center comes out clean. Transfer to a wire rack to cool 15 minutes in pan; remove from pan to cool completely. Stir together remaining 1/3 cup yogurt and confectioner's sugar. Just before serving, drizzle glaze over cake set on wire rack. Slice into 10 pieces.