Heat oven to 350°F.
Into large bowl, break up cookie dough. Add gingersnap crumbs, ginger, cinnamon and 2 1/4 teaspoons orange peel. (Your clean hands will work best to fully combine all the ingredients.)
Shape dough into about 2-inch balls; roll in brown sugar, making sure to evenly coat. Place about 2 inches apart on ungreased cookie sheets.
Bake about 12 minutes or until golden brown. Remove from cookie sheets to cooling racks. Cool.
While cookies are cooling, in medium bowl, stir together Rum Glaze ingredients until thick and smooth. If needed, add a little water for drizzling consistency. Use fork to drizzle glaze over cooled cookies.