Preheat oven to 350 degrees F. Grease the bottom only of two 8x4 inch loaf pans or line the bottoms with strips of parchment**.
In a small mixing bowl, beat the cream cheese and sugar until smooth. Stir in the egg and vanilla. Set aside.
Mix the flour, baking soda,baking powder, salt, cinnamon and nutmeg together in a bowl and set aside.
In a mixing bowl, stir together the sugar, eggs, oil, zucchini and vanilla.
Add the flour mixture to the wet ingredients and stir until mixed.
Pour about ½ of the batter into two greased loaf pans.
Spoon a line of cream cheese batter down the zucchini bread batter, dividing evenly between the two pans.
Cover cream cheese mixture with remaining batter.
Bake in the lower third of the oven for 55 -60 minutes or until a toothpick inserted near the center comes out clean.
Let cool for 15 minutes. Loosen sides of loaves with a knife, then carefully turn from pan and let cool completely before slicing.
Notes
My preferred method is to line the pans with a narrow strip of parchment paper that goes the length of the bottom of the pans and up the short sides. Theoretically, the sides of the loaf pan should be left ungreased, as this is supposed to help the batter cling to the pan and rise upward instead of inward. The loaves will dome nicely.