Heat oven to 350 degrees. Cake: Coat a 13 x 9 x 2-inch baking pan with nonstick cooking spray. Line bottom with parchment or wax paper. Coat paper with spray.
In a medium bowl, whisk together flour, cinnamon, ginger, baking soda and nutmeg. In a large bowl, beat butter until creamy. Beat in brown sugar and maple syrup. Beat in eggs (mixture will look slightly curdled). On low speed, beat in half the flour mixture, then the sour cream mixture and ending with the remaining flour mixture. Stir in maple flavoring. Transfer to prepared pan and spread level. Bake at 350 degrees for 30 minutes, or until toothpick inserted in center of cake tests clean. Cool in pan for 5 minutes on wire rack. Remove from pan and remove wax paper. Cool completely.
Meanwhile, make Frosting. Beat together butter and cream cheese in a large bowl. Sift in confectioners' sugar. Add milk and maple flavoring. Beat on low speed until smooth and good spreading consistency.
Cut cake in half crosswise, then split each half horizontally to create 4 thin layers. Place 1 layer on a platter. Spread with 2/3 cup of the frosting. Sprinkle with 1/4 cup of the walnuts, if desired. Repeat twice. Top final layer with cinnamon sticks or additional walnuts, if desired.