Preheat the oven to 350°F and line an 8×4-inch loaf pan with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In another large bowl, place the sugar and lemon zest and use your fingers to rub them together until well blended and fragrant. Add the eggs, oil, yogurt, and vanilla, and whisk to combine.
Transfer the dry ingredients on top of the wet ingredients and mix with a spatula until no streaks remain. Fold in the zucchini.
Transfer the batter into the prepared pan, smooth out the top, and bake for 50-60 minutes, or until a toothpick inserted in the center of the loaf comes out clean. If necessary, tent the pan with foil after 45 minutes of baking to prevent the top from browning too much.
Remove from the oven and allow the bread to cool completely in the pan, set on a wire rack. Once cooled, remove the loaf.
Meanwhile, make the glaze. Whisk all ingredients until smooth. Drizzle glaze over cooled bread and serve immediately.