Preheat oven to 400°F. Line a baking sheet with parchment paper; set aside.
In a large bowl, whisk together the flour, baking powder, salt, brown sugar, ginger, cinnamon, and cloves. Using a pastry blender, cut butter into flour mixture until mixture resembles coarse meal.
In a medium bowl, whisk together the buttermilk and molasses. Add buttermilk mixture to flour mixture and stir until dough is just combined (the dough will be sticky).
Transfer dough to a lightly floured surface and pat to ½-inch thickness. Using a small star cutter, cut out 30 scones, gathering scraps and rerolling as necessary. (See Baking Tip #1 for easy method of cutting sticky dough.)
Place scones on the prepared baking sheet. Brush the tops of scones with beaten egg. Sprinkle the candied ginger pieces onto the tops of the stars.
Bake for 14 – 15 minutes, or until golden brown. Transfer to wire rack to cool.
For the frosting, beat the butter, powdered sugar, and heavy cream together until smooth. Use more heavy cream to make it creamier and easier to pipe. Pipe on completely cooled dessert.