Preheat oven to 350°F (175°C) and line two large baking sheets with parchment paper.
In a medium mixing bowl, whisk together the flour, ginger, cinnamon, cloves, nutmeg, baking soda, and salt.
In a large bowl or stand mixer, cream the butter and brown sugar until light and fluffy, approximately 3 minutes.
Add the egg, molasses, vanilla extract, and 1 tablespoon of espresso powder to the butter mixture; beat until fully incorporated.
Slowly add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined.
Scoop approximately 1.5 tablespoons of dough per cookie and roll into balls. Place on the prepared baking sheets spaced 2 inches apart.
Bake for 8 to 10 minutes until the edges are set and the tops are slightly cracked.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Prepare the glaze by whisking confectioners' sugar, milk, and 1/2 teaspoon espresso powder until smooth.
Drizzle the espresso glaze over the cooled cookies and let set for 15 minutes before serving.