Make the cheesecake filling: In a small bowl, beat cream cheese, powdered sugar, and vanilla until smooth. Scoop 12 small teaspoons of filling onto a parchment-lined plate and freeze for at least 30 minutes.
Blot the pumpkin puree: Measure out your pumpkin puree, then use a paper towel to blot as much moisture out of the pumpkin puree as possible.
Mix the dry ingredients: In a medium bowl, whisk flour, baking powder, baking soda, salt, and pumpkin pie spice.
Make the cookie dough: In a large bowl, beat butter, brown sugar, and granulated sugar until light and fluffy (2–3 minutes). Mix in blotted pumpkin purée, egg yolk, and vanilla. Fold in the dry ingredients until just combined. Chill the dough for 30 minutes for easier handling.
Assemble the cookies: Scoop about 2 tablespoons of dough, flatten slightly, place a frozen cheesecake ball in the center, and wrap dough around it, sealing completely. Roll in cinnamon sugar if desired.
Bake: Arrange on a parchment-lined tray and bake at 350°F (175°C) for 11–13 minutes, until edges are set but centers look slightly soft. Cool on the tray for 5 minutes before transferring to a rack.