Start by lining two large baking sheets with parchment paper and preheating your oven to 350 degrees Fahrenheit. In a small bowl, combine the softened cream cheese, powdered sugar, and the second portion of alcohol-free vanilla. Stir until the mixture is completely smooth. Drop small teaspoons of the filling onto a plate and place them in the freezer for about 20 minutes to firm up.
In a large mixing bowl, beat the softened butter and brown sugar together until the mixture is light and fluffy. Add the egg, molasses, and alcohol-free vanilla, continuing to mix until everything is well combined. Make sure to scrape down the sides of the bowl so the molasses is evenly distributed.
In a separate medium bowl, whisk together the flour, baking soda, ground ginger, cinnamon, cloves, nutmeg, and salt. Gradually add these dry ingredients to the wet mixture, stirring on a low speed until a soft dough forms. Do not overmix, as this can make the cookies tough.
Take about a tablespoon of gingerbread dough and flatten it in your palm. Retrieve the chilled cream cheese balls from the freezer. Place one cream cheese ball in the center of the dough and wrap the dough around it, pinching the edges to seal the filling completely inside. Roll the ball between your palms to make it smooth.
Roll each stuffed dough ball in the granulated sugar until it is evenly coated. Place the balls on the prepared baking sheets, leaving about two inches of space between them. Bake for 10 to 12 minutes, or until the edges are set but the centers still look slightly soft. Let them cool on the pan for five minutes before moving them to a wire rack.