Whisk together first 5 ingredients in a bowl; set aside.
Beat butter and brown sugar in a large bowl at medium-high speed with an electric mixer until creamy. Add egg; beat until blended. Add molasses and grated ginger; beat until well blended. Add flour mixture and buttermilk alternately, beginning and ending with dry ingredients. Spread batter into a greased and floured 8" pan.
Bake at 350° for 40 to 42 minutes or until a wooden pick inserted in center comes out clean. Cool in pan on a wire rack 10 minutes. Carefully transfer cake to cooling rack; cool completely. Wrap cake in plastic wrap; chill 8 hours or overnight.
Beat cream cheese and powdered sugar at medium speed until fluffy. Stir in 1/8 teaspoon ginger, pinch of cinnamon, and pinch of allspice. Cut cake in half horizontally, making 2 equal layers. Spread frosting evenly over bottom cake layer. Carefully place remaining cake layer on frosting. Cut cake into 25 squares, using a serrated or an electric knife. Place squares on a rack over a baking sheet.
Remove foil cover from frosting containers. Microwave frosting at HIGH 30 seconds or until melted, stirring once. Pour or spoon frosting over petits fours, coating top and sides completely. If additional frosting is needed, scrape excess frosting from baking sheet and return to container, and microwave on HIGH 15 seconds or until melted. Place petits fours in large candy cups, if desired. Store in an airtight container in refrigerator.