Line a small baking sheet or plate with parchment paper. In a medium bowl, beat the softened cream cheese, powdered sugar, vanilla extract, and salt until smooth.

Spoon 12 small portions of cream cheese filling, about 2 teaspoons each, onto the parchment-lined tray. Freeze for at least 45 minutes, until firm.

In a medium bowl, whisk together flour, pumpkin pie spice, baking soda, baking powder, and salt.

In a large bowl, beat the softened butter, brown sugar, and granulated sugar until creamy, about 2 minutes.

Add the egg yolk and vanilla extract. Beat until combined. Add the pumpkin butter and mix until smooth.

Add the dry ingredients to the pumpkin butter mixture. Mix on low speed just until no dry flour remains. Cover the dough and refrigerate for at least 30 minutes.

Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.

If using the cinnamon sugar coating, combine the granulated sugar and cinnamon in a small bowl.

Scoop about 3 tablespoons of chilled cookie dough and flatten it into a thick disc. Place one frozen cream cheese filling portion in the center. Bring the dough around the filling, pinch the edges closed, and roll gently into a ball. Make sure no filling is visible.

Roll the cookie dough ball in cinnamon sugar if using. Place it seam-side down on the prepared baking sheet. Repeat with the remaining dough and filling, spacing cookies at least 3 inches apart.

Bake for 11 to 14 minutes, until the edges are set and the tops are puffed and lightly cracked. The centers should still look slightly soft.

Let the cookies cool on the baking sheet for 10 to 15 minutes before transferring them to a wire rack. Cool completely, then refrigerate in an airtight container.