In a medium bowl, whisk together flour, baking soda, baking powder, salt and cinnamon until just incorporated. Set aside.
Cream the cream cheese and sugar on medium speed for 2 minutes. Add eggs one at a time, mixing for one minute after each addition. Mix in vanilla. Pour in melted butter and mix. Beat for 3 minutes with mixer on medium-high.
Carefully mix in flour mixture. Add zucchini and mix just until incorporated.
Make the cinnamon swirl by stirring cinnamon and sugar together in small bowl. Pour half of cake batter into prepared bundt pan. Sprinkle cinnamon swirl mixture over batter. Top with the rest of the batter. Tap the pan a few times to release any air bubbles.
Bake for 50 to 60 minutes or until a toothpick inserted in the cake comes out with little to no crumbs. Remove from oven and cool for 20 minutes. Then turn onto a wire rack and let it cool completely.
To make the glaze, mix confectioners' sugar and cinnamon together in a small bowl. Mix in milk and vanilla. Drizzle glaze over cake, slice and serve.
Notes
Greasing a bundt pan: Be generous with the butter and get into all the nooks and crannies, then dust with flour. I like to use this cake paste, which guarantees the cake won't stick.Zucchini: Make sure it is fresh otherwise it might leave a subtle bitter taste in your baked goods. Leave the skin on when shredded with a box grater.Store in an airtight container at room temperature for 3 or 4 days.Freeze for up to 3 months. Wrap the cake (or slices) in plastic wrap and place in an airtight container. Freeze and, when ready to eat, defrost in the refrigerator before bringing to room temperature.