MAKE THE MUFFINS. Preheat the oven to 350 degrees and line a 12-cavity cupcake mold with aluminum liners; spray the exposed pan and liners with baking spray.
In a medium sized bowl, whisk the flour, candied ginger, cinnamon, ground ginger, cloves, baking powder, baking soda and salt until well combined; set aside.
In a large bowl, whisk the 2 eggs, milk, oil and vanilla until well combined and emulsified.
Add the sugar, brown sugar and molasses, and whisk to combine.
Add the dry ingredients and stir until just combined.
Scoop or pipe the batter into the prepared liners, filling each ¾ full.
Bake until a toothpick comes out clean when inserted into the center of the muffins, for 35-40 minutes; carefully transfer to a rack and cool completely.
MAKE THE ICING. In a medium-sized bowl, stir the egg white and sugar until a smooth, stiff frosting forms; it should hold a peak. If it is too loose, add some more sugar to reach the desired consistency. If it is too thick, add a splash of water to reach the desired consistency.
Working fast, spread the icing over the muffins and decorate with sprinkles.