Preheat the oven to 350 degrees F. Grease and flour a Bundt pan and set aside.
In a medium-sized bowl, whisk together the flour, baking soda, baking powder, salt, and cinnamon. Set aside.
In the bowl of a stand mixer, cream the cream cheese and sugar together for 2 minutes. Add the eggs one at a time, mixing well between additions.
Add the vanilla extract and melted butter. Beat for 3 minutes.
In 2 batches, add the flour mixture until it is just incorporated. Add the shredded zucchini and mix again until just incorporated.
Mix the sugar and cinnamon together in a small bowl.
Pour half of the cake batter into the prepared Bundt pan. Sprinkle the cinnamon sugar mixture evenly over the batter. Top with the remaining batter and smooth with a spatula.
Bake for 1 hour, or until a knife/toothpick comes out clean when inserted into the center. Allow the cake to cool in the pan for 20 minutes before turning the cake out onto a wire rack to cool completely.
Whisk all ingredients together in a small bowl. Add more milk if you want a thinner glaze. Drizzle the glaze over the cooled cake.