To prepare cake, place 1/3 cup granulated sugar and butter in a medium bowl; beat with a mixer at high speed for 2 minutes or until well combined. Add molasses and egg; beat well.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 5 ingredients (through cloves) in a medium bowl. Add flour mixture and milk alternately to sugar mixture, beginning and ending with flour mixture. Stir in 1 teaspoon vanilla. Spoon batter into an 8-inch square pan coated with cooking spray. Bake at 350° for 30 minutes or until a wooden pick inserted in the center comes out clean. Cool completely on a wire rack.
To prepare frosting, place cheeses, 1 teaspoon vanilla, and 1/8 teaspoon salt in a large bowl; beat with a mixer at medium speed until light and fluffy. Gradually add powdered sugar; beat at low speed just until blended (do not overbeat). Spread frosting evenly over top of cake. Top each serving with Lemon Curd.