In the bowl of a mixer, mix together the brown sugar, eggs, applesauce, molasses, vegetable oil and milk until completely combined. Add in the dry ingredients and mix just until combined. Transfer the batter to a ziptop bag. Cut off the corner and pipe the dough into the prepared donut pan, filling 2/3 full.
1/2 cup brown sugar, 2 eggs, 1/4 cup applesauce, 1/4 cup molasses, 4 tablespoons vegetable oil, 2 tablespoons milk
Bake until a toothpick inserted in the center comes out clean, about 10 minutes. Cool for 10 minutes then turn out onto a cooling rack to cool completely.
Once cool, make the glaze. In a small bowl, combine all glaze ingredients and dip the tops of the donuts into the glaze. Return to the cooling rack to let the glaze set up.