1. MAKE THE CHEESECAKE FILLING: In a medium bowl, beat the cream cheese until smooth and free of lumps. Add the granulated sugar, vanilla extract, and flour, and mix until the filling is completely smooth. Transfer the mixture to a piping bag or a zip-top bag with one corner snipped off. Chill in the refrigerator for at least 30 minutes while preparing the cookie dough.

2. MAKE THE PUMPKIN COOKIE DOUGH: In a large bowl, beat together the butter, brown sugar, and granulated sugar until light and fluffy, about 2 to 3 minutes. Add the pumpkin puree, egg, and vanilla extract and mix until well combined. In a separate bowl, whisk together the flour, baking soda, baking powder, salt, pumpkin pie spice, and cinnamon. Gradually mix the dry ingredients into the wet ingredients until a soft dough forms. Cover and chill the dough for 30 minutes to help the cookies keep their shape while baking.

3. SHAPE AND BAKE THE COOKIES: Preheat the oven to 350°F (175°C) and line two baking sheets with parchment paper. Scoop about 2 tablespoons of dough for each cookie and roll into balls. Place the dough balls 2 inches apart on the prepared baking sheets. Flatten each one slightly, then use your thumb or the back of a spoon to press a shallow well into the center of each dough ball. Bake for 12 to 14 minutes, or until the edges are set and the tops look just done. Remove from the oven and, if needed, use the back of a spoon to gently press down the centers again. Allow the cookies to cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.

4. FILL WITH CHEESECAKE: Once the cookies are fully cooled, pipe about 1 to 1½ teaspoons of the chilled cheesecake filling into the center of each cookie. Smooth the top if desired. Chill the filled cookies in the refrigerator for 20 minutes to allow the filling to set before serving.