Preheat the oven to 350°F.
In a small or medium-sized bowl, whisk together the flour, ginger, baking soda, cinnamon, salt, and allspice. Set Aside
In a large mixing bowl, beat the butter and brown sugar on medium-high until creamy.
Add in the molasses and egg. Scrape down the side of the bowl.
Gradually beat in the flour mixture until just combined.
Using a small cookie scoop evenly portion out the cookie dough, spacing them 2 inches apart.
Bake the cookies for 10-12 mins or until the edges of the cookies are set.
Cool on the cookie sheet for 10 min.
Flip the cookies overexposing the bottom side or place them on a cooling rack.
Once the cookies are completely cooled mix the icing.