For the cake: Preheat the oven to 350 degrees F. Grease a 9-by-13-inch pan.
In a large bowl, whisk together the flour, granulated sugar, pecans, coconut, baking soda, cinnamon, salt, nutmeg and ginger. In another bowl, whisk together the oil, milk, vanilla and eggs and stir in the grated zucchini. Fold this into the dry ingredients. The batter will be stiff and dry but keep folding it and it will all come together. If it still seems too dry, just add a little more milk.
Spread the batter into the prepared pan. Bake until a wooden pick inserted in the center comes out with moist crumbs and the cake is pulling away from the sides of the pan, about 20 minutes. Cool completely on a wire rack.
For the frosting: Beat the cream cheese and butter in a large bowl with a mixer at medium speed until smooth. Beat in the powdered sugar and vanilla just until smooth. Add the milk if necessary.
Spread the frosting over the top of the cooled cake. Garnish with chopped pecans.
If your zucchini are huge, scrape the seeds out of the center before you shred it so it's not too watery.
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