In a medium bowl, beat the 6 oz softened cream cheese, 1/3 cup powdered sugar, and 1 tsp vanilla until smooth. Scoop 1/2 tablespoon sized dollops onto a wax paper-lined plate and smooth into a round disc. Freeze for 2 hours, or until firm.
In a bowl, whisk together the 2 1/2 cups flour, 1 tsp baking soda, 1 tbsp ginger, 1 tbsp cinnamon, 1/4 tsp cloves, 1/4 tsp nutmeg, and 1/2 tsp salt.
In the bowl of a stand mixer affixed with a paddle attachment, cream together the 1/2 cup softened butter, 1/2 cup sugar and 3/4 cup brown sugar until light and fluffy. Beat in the 1 whole egg, 1 egg yolk, 1/3 cup molasses, and 2 tsp vanilla, just until mixed.
Add half the dry ingredients to the wet, mix, add the remaining dry ingredients and mix just until combined. Chill the dough for 2 hours or overnight.
Take the cream cheese dollops out of the freezer about 10 minutes before shaping cookies. Scoop about 2 tablespoons of cookie dough and flatten into a disc between your palms. Place a frozen cheesecake disc in the center and wrap the dough around it, sealing completely. Roll dough ball in granulated sugar.
Preheat oven to 350°F. Place cookies on a lined baking sheet, spacing them a few inches apart. Bake for 13-14 minutes, or until the edges are set and tops are slightly cracked. Cool completely on the tray before moving.