01 - Preheat oven to 350°F. Grease and line an 8-inch square cake pan with parchment paper.
02 - In a medium bowl, whisk together the gluten-free flour, baking powder, baking soda, salt, ginger, cinnamon, and cloves until well blended.
03 - In a large bowl, beat the butter and brown sugar until light and fluffy, approximately 2-3 minutes.
04 - Add eggs one at a time, mixing thoroughly after each addition. Stir in applesauce, milk, molasses, and vanilla extract until combined.
05 - Gradually fold in the dry ingredients until just combined. Take care not to overmix the batter.
06 - Transfer the batter to the prepared pan and smooth the top surface evenly.
07 - Bake for 30-35 minutes, or until a toothpick inserted into the center emerges clean.
08 - Allow the cake to cool completely in the pan on a wire rack before frosting.
09 - Beat together cream cheese and butter until smooth. Add powdered sugar, vanilla, and salt; continue beating until creamy and uniform.
10 - Spread frosting evenly over the cooled cake. Slice into portions and serve.