Preheat an oven to 325 degrees F (165 degrees C). Spray 2 9×5-inch loaf pans with cooking spray.
In a large bowl, mix together the brown sugar, molasses, vegetable oil, vanilla yogurt, and eggs until thoroughly combined. Stir in the cinnamon, ginger, nutmeg, cloves, baking soda, baking powder, and salt. Gently mix in the shredded zucchini, and stir in the flour. Pour the batter into the prepared loaf pans.
Bake in the preheated oven until the loaves are browned and springy to the touch, 50 to 60 minutes. A toothpick inserted into the center of a loaf should come out clean. Allow to cool in pans for about 10 minutes before removing to finish cooling on racks.
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