Apple Ginger Cake

2/3 cup light brown sugar
1/3 cup applesauce
1 large egg
3 Tbsp. molasses
1-1/2 cup all-purpose flour
1 tsp. baking powder
1 tsp. baking soda
1 tsp. cinnamon
2 tsp. ground ginger
1/4 tsp. nutmeg
1/8 tsp. allspice