Preheat oven to 325° F. Grease an 8-inch square pan. Whisk together oil, brown sugar, eggs, maple syrup and grated ginger. In a separate bowl, sift flour, baking powder, baking soda, salt and cinnamon and stir into wet mixture to blend. Stir in carrot and pineapple and pour into prepared pan. Bake for 1 hour and 15 to 30 minutes, until a tester inserted in the center of the cake comes out clean. Allow to cool completely before icing.
To prepare frosting, beat cream cheese and butter together. Beat in icing sugar until smooth and stir in vanilla. Spread over cooled cake and store chilled until ready to serve.
Yield: 1 8-inch square cake. Makes 9 to 12 servings.