Preheat the oven to 350 degrees. Spray two 9-inch round cake pans with baking spray and set aside.
In a large bowl, whisk together the flour, gingers, lemon zest, salt, baking soda and baking powder. In a medium bowl, whisk together the zucchini, olive oil, honey, eggs, and vanilla. Make a well in the center of the dry ingredients, add the wet ingredients, and mix well until just combined.
Divide the batter evenly between the prepared cake pans. Bake until the cakes are golden, and a cake tester inserted into the center of a cake comes out clean, about 30 minutes.
Cool the cakes in the pans for about 10 minutes, then remove them from the pans and allow to cool completely on a cooling rack.
While the cakes are cooling, make the frosting. In the bowl of a stand mixer, beat the cream cheese and butter on medium speed until smooth. Add the powdered sugar, then the vanilla and ginger. Beat on high until the frosting is light and fluffy.
Place one of the cakes on a platter,top side down, and spread a thin layer of frosting all over the top. Add the second cake on top and press gently. Spread the rest of the frosting all over the top of the cake, allowing it to drip down the sides as well. Cut into slices and serve.