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.
In a large mixing bowl, beat the softened butter and sugars until light and fluffy.
Add the egg and vanilla to the butter mixture; continue beating until well combined.
Gradually add the dry ingredient mixture to the wet mixture; mix until just combined.
In a separate bowl, beat the cream cheese until smooth; add powdered sugar and lemon juice, mixing until creamy.
Scoop out a tablespoon of cookie dough and flatten it slightly. Place a teaspoon of the cream cheese filling in the center, then cover with another tablespoon of dough, sealing the edges.
Place filled cookies on the prepared baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for 12-15 minutes or until the edges are lightly golden.
Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.