Make the cheesecake filling: In a small bowl, beat 8 oz cream cheese with 1/3 cup powdered sugar and 1 teaspoon vanilla until smooth and thick. Scoop 18–20 heaping teaspoon-sized mounds onto a parchment-lined plate.
Freeze 20–30 minutes, until firm but not rock-hard.
Preheat and prep pans: Heat oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone mats.
Mix dry ingredients: In a medium bowl, whisk 2 1/2 cups flour, 1 teaspoon baking soda, 1/2 teaspoon salt, 2 teaspoons ground ginger, 1 1/2 teaspoons cinnamon, and 1/4 teaspoon cloves. Set aside.
Cream butter and sugars: In a large bowl, beat 3/4 cup softened unsalted butter with 3/4 cup dark brown sugar and 1/4 cup granulated sugar until light and fluffy, about 2 minutes.
Add wet ingredients: Beat in 1 egg and 1/3 cup molasses until smooth.
Scrape the bowl.
Combine: Add dry ingredients to wet and mix on low just until no dry streaks remain. Dough will be soft and slightly sticky.
Portion dough: Scoop 18–20 portions (about 1 1/2 tablespoons each). Roll into balls.
Flatten each ball into a thick disk in your palm.
Stuff with cheesecake: Place a frozen cheesecake mound in the center of a dough disk. Wrap dough around it, pinching seams to seal completely. Roll gently back into a ball.
Coat in sugar: Roll each stuffed ball in granulated sugar for a light, even coat.
Arrange on prepared sheets, spacing 2 inches apart.
Bake: Bake 10–12 minutes, until edges are set and tops crackle slightly. Centers should look puffed and just set—avoid overbaking.
Cool: Let cookies cool on the sheet for 10 minutes (the centers finish setting), then move to a wire rack to cool completely.
Optional drizzle: For extra flair, whisk 1/2 cup powdered sugar with 1–2 teaspoons milk and a drop of vanilla. Drizzle over cooled cookies.