Preheat oven to 350 degrees F. Spray an 8-inch square cake pan with cooking spray and line the bottom with parchment paper. Spray the parchment with cooking spray as well, and then set aside.
In a small saucepan, combine the butter and milk. Heat over medium-high, just until the butter is melted and bubbles form around the edges of the pan. Whisk in the brown sugar until dissolved. Remove from the heat and cool.
In a large bowl, sift together flour, baking soda, baking powder, ginger, cinnamon, cloves and salt.
Stir the egg into the cooled butter mixture.
Make a well in the center of the dry ingredients and pour in the butter mixture. Stir just until a smooth batter forms, being careful not to over-mix.
Pour the batter into the prepared pan. Bake until a toothpick inserted in the center comes out clean, about 25-30 minutes. Cool completely on a wire rack before slicing and serving.
Dust cooled cake with powdered sugar and serve with whipped cream, if desired.