Preheat oven to 350°F. Grease and flour a 9x5” loaf pan, set aside.
Place the shredded zucchini on a paper towel and lightly dab the zucchini so that it's not so wet. Don't ring it out; we just don't want the zucchini to be sopping wet.
In a medium size bowl combine the sugar and lemon zest. Using your fingers, rub the lemon zest and sugar between your fingers until the lemon zest has been evenly combined in the sugar. Add the eggs and oil to the sugar. Beat on medium speed for 2 minutes or until slightly lighter in color.
Add the vanilla and mix until combined.
In a medium sized bowl whisk the flour, baking powder, and salt. Pour half of the dry ingredients into the egg and sugar mixture. Mix until barely combined, there will be streaks of flour remaining. With the mixer on low, add the sour cream and the remaining flour mixture. Mix until just combined, do not over mix.
Using a rubber spatula, fold in the zucchini.
Pour the batter into the loaf pan and bake for 55-60 minutes, or until a toothpick inserted in the center of the loaf comes out clean.
Remove from oven and cool on wire rack for 5-10 minutes, then remove from the bread pan and cool on wire rack completely.