Preheat the oven to 350°F (175°C).
In a bowl, whisk together the flour, baking soda, ginger, cinnamon, cloves, and nutmeg.
In a separate bowl, beat the softened butter, granulated sugar, and brown sugar until creamy.
Add the egg and vanilla extract to the butter mixture; beat until combined.
Gradually add the dry mixture to the wet ingredients, mixing until just combined.
In another bowl, beat the softened cream cheese and powdered sugar until smooth.
Scoop cookie dough onto baking sheets lined with parchment paper, making an indentation in each cookie.
Fill each indentation with about one teaspoon of the cream cheese mixture.
Bake for 12-15 minutes or until edges are lightly golden.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.