In a medium bowl, whisk together the flour, baking soda, baking powder, salt, and cinnamon. Set aside.
In the bowl of a stand mixer (or with an electric hand mixer), beat cream cheese and sugar on medium speed until well incorporated. Add the eggs, one at a time, beating for 1 minute between each addition, then add the vanilla extract. With the mixer on low speed, pour in the melted butter and increase the speed to medium-high. Continue mixing about 3 more minutes, until the batter is shiny and smooth.
Reduce the speed to low and add the flour mixture all at once. It's important not to over-mix the batter, so beat just until incorporated (there will still be some flour present in the batter). Add the zucchini and use a spatula to fold it in and finish incorporating the flour into the batter. The batter will be thick.
Using a small pastry brush or spatula, "paint" the melted chocolate on the inside of the bundt pan.
Spoon the batter into the pan and bake for 45-50 minutes, until a skewer inserted near the center comes out with just a few crumbs. Remove cake from the oven and allow it to cool in the pan for 20 minutes before inverting onto a wire rack to cool completely.
If desired, dust with powdered sugar.
Notes
Recipe adapted from Zucchini Cream Cheese Pound Cake, by Joy Wilson (Joy the Baker). Source: Joy the Baker's Cookbook - 100 Simple & Comforting Recipes.This recipe will fill a 12-cup bundt cake or two 9-inch x 2-inch round cake pans