Cut butter into Tablespoon-sized pieces and place in a large, microwave-safe mixing bowl. Heat in 15-second intervals until butter is melted then immediately stir in ginger, cinnamon, cloves, nutmeg, and allspice. Stir well and allow butter to cool before proceeding.
Once butter is cooled (no longer warm to the touch) add sugars, egg, egg yolk, and vanilla and stir until completely combined.
In a separate medium-sized bowl, whisk together flour, cornstarch, baking soda, baking powder, and salt.
Gradually add dry ingredients to wet. Stir until completely combined.
Cover cookie dough with plastic wrap and chill in the refrigerator for at least 30 and preferably 60 minutes. Meanwhile, preheat oven to 350F (175C) and line baking sheets with parchment paper.
Once dough has finished chilling, scoop by level 1 ½ tablespoon-sized scoop and roll into a ball between your palms. Place cookie dough balls on prepared baking sheet, spacing at least 2 inches apart.
Bake at 350F (175C) for 11-12 minutes or until edges are beginning to turn a light golden brown. Allow to cool completely before decorating with glaze.
Glaze: In a small mixing bowl, whisk together powdered sugar, vanilla, and 1 tablespoon of milk. Add more milk as needed, glaze should be smooth and ribbon of your whisk, holding its shape for several seconds before dissolving into the bowl.
Drizzle glaze over cookies and allow to harden. Serve and enjoy.