Prep: Line a baking sheet with parchment paper. Line a small cutting board with parchment paper. This second board will be used to chill the cookie dough so it can be any flat surface like a plate or another baking sheet. Set aside.
Flour mixture: In a medium bowl, stir together the flour, baking soda, cinnamon, ginger, cloves, nutmeg, and salt. Set aside.
Butter mixture: In a large mixing bowl, add the softened butter. Use a hand mixer to beat the butter until it becomes very creamy. Add the brown sugar and granulated sugar. Beat until creamy and fluffy.
Add wet ingredients: Add the molasses and beat again until thoroughly combined. Finally, add the egg and vanilla extract and mix again on low speed until combined.
Combine flour and butter mixtures: Add the flour mixture and mix on low speed until mostly combined. Switch to a spatula to finish mixing to avoid overmixing.
Scoop cookie dough: Use a 4-tablespoon cookie scooper to scoop the cookie dough. Release the cookie dough balls on your lined board. They can be placed close together.
Chill dough: Chill the cookie dough in the fridge for at least 2 hours or overnight until solid.
Prep: Preheat the oven to 350°F. Add the granulated sugar for rolling to a shallow dish.
Stuff the cookie dough with cheesecake: You can do this in two ways. 1) Press the cookie dough with your fingers until it becomes a flat sheet. Place the frozen cheesecake dollop in the middle and wrap it up by bringing the cookie dough back up around the cheesecake. 2) Split the cookie dough in half. Flatten each half separately into two flat rounds. Place the cheesecake dollop on top of one round. Place the other round on top and pinch the dough together to seal.
Roll in sugar: Roll the cookie dough ball in between your hands and then roll it in granulated sugar until coated. Place the dough ball on your lined baking sheet, leaving about 2" in between each ball to account for spreading.
Bake: Bake cookies for 10-11 minutes or until the edges are set and the surface is puffy and slightly cracked.
Cool: Let the cookies cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely.