Beat the cream cheese and the sugar together until smooth, add the egg and vanilla, stir to combine.
Preheat the oven to 350˚F (176°C). Drain the grated zucchini and squeeze out as much water as possible. Set aside.
Lightly grease two 8x4-inch (20 x 10cm) loaf pans. Melt the butter, let it cool but not solidify, then stir in the sugar. Beat in the eggs, vanilla, cinnamon and add the zucchini, stir to combine well.
Add the all-purpose flour, salt and baking soda and baking powder in a separate bowl. Add the milk (or buttermilk) alternately with the flour mixture, stirring to combine, it will be lumpy.
Pour batter in to cover the bottom of the pans, carefully divide the cheesecake batter between the two loaf pans, spread to the edges of the pans.
Cover the cheesecake batter with the remaining batter.
Bake for 45-55 minutes or until a cake tester comes out dry. Cool completely before serving.