Grease 9 x 9" baking pan and set aside.
Preheat oven to 350℉.
Using a grater or food processor, grate zucchini, measure. Add to colander to remove as much liquid as possible. NOTE: use a paper towel to squeeze excess liquid, if desired.
Zest lemon and measure all other ingredients.
In separate bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
In a mixer bowl, using a mixer, cream softened butter and sugar until mixture is light and fluffy.
Add in eggs, one at a time, mixing in each.
Add fresh lemon zest and juice and vanilla extract until all ingredients are well mixed.
Don't use the mixer for this step. Gradually fold in dry ingredients into the wet mixture, stirring gently to keep mixture light and fluffy.
Carefully fold in the grated zucchini until it's evenly distributed throughout the batter.
Pour batter into the greased pan, spreading out evenly into corners.
Bake in preheated oven for 30 minutes or until cake tester comes out clean.
While cake is cooling, add milk, lemon juice and lemon zest, if preferred to powdered sugar to a small bowl to desired glaze consistency.
Mix until smooth.
Drizzle glaze over the cooled zucchini cake, creating a beautiful finish. Feel free to sprinkle with additional lemon or lime zest, if desired.
Allow the glaze to set before cutting the cake into squares for serving. Enjoy!