Preheat oven to 325 degree F. Spray a 12-cup bundt pan with baking spray. Set aside.
Prepare the zucchini: With a cheese grater, grate the zucchini up and down over a bowl. Continue until the entire zucchini is shredded. You can also use a food processor fitted with a shredding attachment. Lay on a flat surface or cutting board and press down with a paper towel on top to absorb any water.
In a large mixing bowl, beat sugar, oil, eggs, and vanilla until blended. Add in flour, baking soda, baking powder, cinnamon, cardamom, and salt for 3 minutes.
Fold in shredded zucchini. Pour into prepared bundt pan.
Bake for 55-60 minutes. Remove and cool in pan 5 minutes before inverting onto a cake plate to cool completely before adding the glaze.
Make the glaze: Whisk together the sugar, cinnamon, vanilla, and milk until smooth. Drizzle over cake. If you have extra glaze you can serve it separately in a bowl to add to individual serving.