Make the cheesecake filling: In a bowl, beat the cream cheese, sugar, vanilla, and salt until smooth and fluffy.
It should be completely lump-free. Scoop into 1-teaspoon mounds onto a parchment-lined plate or small tray. Freeze for 45–60 minutes, until firm but not rock solid.
Whisk the dry ingredients: In a medium bowl, whisk flour, ginger, cinnamon, cloves, nutmeg (if using), baking soda, and salt.
Set aside.
Cream the butter and sugars: In a large bowl, beat the softened butter, brown sugar, and granulated sugar on medium-high for 2–3 minutes, until light and fluffy. Scrape the bowl.
Add egg, molasses, and vanilla: Mix in the egg, then the molasses and vanilla until smooth. The mixture may look slightly separated—that’s okay.
Scrape the bowl again.
Add dry ingredients: Add the flour mixture and mix on low just until no dry streaks remain. Do not overmix. Cover and chill the dough for 30–45 minutes to make it easier to handle.
Prep to bake: Heat oven to 350°F (175°C).
Line two baking sheets with parchment. Place rolling sugar in a shallow bowl.
Shape the cookies: Scoop about 1 1/2 tablespoons of dough (a medium cookie scoop). Flatten slightly in your palm, place a frozen cheesecake mound in the center, and wrap dough around it, sealing well.
Roll into a smooth ball, then roll in sugar to coat. Repeat with remaining dough and filling.
Bake: Arrange on baking sheets, spacing 2 inches apart. Bake 10–12 minutes, until the edges look set and the tops crack slightly.
The centers should still look soft; they’ll finish setting as they cool.
Cool: Let cookies rest on the baking sheet for 5–7 minutes, then transfer to a rack to cool fully. The filling firms up as the cookies cool.
Optional finish: Dust cooled cookies lightly with powdered sugar, or drizzle with a simple vanilla glaze for extra sweetness.