Preheat oven to 350 degrees F and line an 8-inch square baking dish with parchment paper.
In a medium bowl, use hand-held electric mixer to beat cream cheese, granulated sugar and flour until smooth.Beat in egg and vanilla just until mixed in. Set aside.
In a clean mixing bowl, beat butter, brown sugar, and granulated sugar until light and fluffy, about 4 minutes.
With mixer on LOW, beat in egg just until combined.
In a medium bowl, whisk together flour, salt, baking powder, baking soda, cinnamon, and nutmeg.
With mixer on LOW, gradually beat flour mixture into the batter.
Add zucchini and chocolate chips and mix on LOW until mixed in.
Transfer a little over half of the batter to the prepared baking pan and spread it evenly in the bottom of the pan.
Top with cheesecake mixture, spreading it evenly.
Spoon remaining batter on top.
Bake for 40 to 45 minutes. Cover with foil after 30 minutes if top is getting browned.Note: The top may look like it is done after 40 minutes but be sure the top layer of batter is fully cooked underneath.
Let cool completely before cutting into squares. I like to refrigerate it first.
Notes
Grate the zucchini on the large holes of a box grater and then place on a triple layer of paper towels. Squeeze zucchini in paper towels to get rid of any liquid.Can be stored in an airtight container in the refrigerator for 5 days or frozen for up to 2 months.