Make sure your butter and egg are at room temperature before beginning.
Preheat the oven to 350 degrees.
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 minutes or until the edges of the cookies are set.
Cool on the cookie sheet for 10 minutes.
Place them on a cooling rack.
Mix the icing by adding the powdered sugar, vanilla and milk to a small bowl.
Stir until combined.
Add in an additional teaspoon of milk until you have a nice thick consistency icing.
Once cookies are completely cool, use a teaspoon to carefully spoon the icing onto the cookies.
Let them air dry until set (about 45 min-hour)