Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
In a large bowl, cream together butter, granulated sugar, and brown sugar until light and fluffy.
Add molasses, egg, and vanilla extract; mix until well combined.
In a separate bowl, whisk together flour, ginger, cinnamon, cloves, nutmeg, baking soda, and salt.
Gradually add dry ingredients to wet ingredients, mixing until just combined.
Scoop 1/3 cup portions of dough, roll into balls, and place on prepared baking sheets, spacing 3 inches apart.
Bake for 10-12 minutes until edges are set but centers remain soft.
Allow cookies to cool completely on the baking sheet.
Prepare frosting by beating cream cheese and powdered sugar together, adding milk as needed for consistency.
Pipe frosting onto cooled cookies in a spiral pattern.