Preheat oven to 350°. Line muffin tins with paper liners.
With an electric mixer, beat together butter, eggs, sugar, and pumpkin puree on low until well blended.
In a separate bowl, whisk together flour, baking soda, baking powder, and spices.
Slowly add the dry mixture to the wet ingredients and mix on low speed until everything is combined and there are no lumps.
Add the shredded zucchini and chocolate chips and stir until just combined.
Scoop into lined muffin pans, filling each with a little under 1/3 cup of the batter.
Bake for 20-25 minutes, until they spring back when touched in the center or a toothpick inserted into the middle comes out clean. Let them cool completely before making the frosting.
To make the frosting, whisk together the powdered sugar, milk, and clear vanilla extract until a thick icing forms with no clumps. If needed, add more sugar or milk to reach your desired consistency.
Dip the tops of each cooled muffin into a bowl with the icing. Sprinkle with a little pumpkin pie spice for an extra garnish if you'd like. Enjoy!