Preheat oven to 400 degrees F.
Line 14 to 15 muffin tins with cupcake liners.In a large mixing bowl combine sugar, brown sugar, molasses, oil, applesauce egg, and vanilla. Mix well.
In a separate bowl sift together flour, baking powder, baking soda, salt, cinnamon, and ginger. Whisk together.
In a small bowl combine the milks.
Alternate adding the flour mixture with the milk mixture until just combined. Do not over mix.
Fill muffins 3/4 of the way full.
Sprinkle with coarse sugar and bake for 10 minutes at 400 degrees F.
After 10 minutes, turn the oven down to 375 degrees F. Bake for another 3 to 5 minutes.
You know they are done when the muffins spring back to the touch. Do not over bake or they will be tough.
Cool on a wire rack.