Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.

In a medium bowl, whisk together the flour, baking soda, ginger, cinnamon, nutmeg, and salt until well combined.

In a large bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.

Add the egg and vanilla extract to the sugar-butter mixture, and mix until well incorporated.

Gradually add the dry ingredient mixture to the wet ingredients, mixing until just combined.

In a separate bowl, beat together the cream cheese, powdered sugar, ground ginger, and cinnamon until smooth and creamy.

Scoop tablespoon-sized amounts of cookie dough onto the prepared baking sheet, spacing them about 2 inches apart.

Make a small indentation in the center of each cookie dough ball using your thumb or the back of a spoon.

Fill each indentation with about a teaspoon of the cream cheese mixture, being careful not to overflow.

Bake in the preheated oven for 12-15 minutes or until the edges are lightly golden and the cookies are set.

Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.