Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking soda, baking powder, ginger, cinnamon, nutmeg, cloves, and salt. Set aside.
In a large mixing bowl, beat the softened butter, brown sugar, and granulated sugar until light and fluffy, about 2-3 minutes.
Add the egg and vanilla extract to the butter mixture and beat until well combined.
Gradually add the dry ingredient mixture to the wet ingredients, mixing just until combined.
In a separate bowl, mix the softened cream cheese, powdered sugar, and milk until smooth and creamy.
Using a cookie scoop or tablespoon, drop a small ball of cookie dough onto the prepared baking sheet. Make a small indentation in the center of each dough ball with your thumb.
Spoon about 1 teaspoon of the cheesecake filling into each indentation of the cookie dough balls.
Bake in the preheated oven for 10-12 minutes or until the edges are slightly golden.
Allow the cookies to cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely.
Notes
Dust the cooled cookies with powdered sugar or drizzle with glaze for a festive touch.