**Prepare the Cheesecake Filling:**
In a medium bowl, beat the cream cheese, sugar, and vanilla extract until smooth. Scoop 1-teaspoon-sized dollops onto a parchment-lined baking sheet and freeze for 1–2 hours, until firm.
**Make the Cookie Dough:**
In a large bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, cloves, and salt. In another large bowl, using an electric mixer, cream the butter, granulated sugar, and brown sugar until light and fluffy. Add the egg, pumpkin puree, and vanilla extract, beating until combined. Gradually mix in the dry ingredients until a soft dough forms.
**Assemble the Cookies:**
Scoop a tablespoon of dough, flatten it slightly, and place a frozen cheesecake dollop in the center. Cover with another tablespoon of dough, sealing the edges to enclose the filling completely.
**Add the Topping (Optional):**
In a small bowl, mix the sugar and cinnamon. Roll each cookie dough ball in the mixture for a spiced sugar coating.
**Bake:**
Preheat oven to 350°F (175°C). Arrange the cookies on parchment-lined baking sheets, spaced 2 inches apart. Bake for 12–15 minutes, or until the edges are set and the tops are slightly puffed. Allow to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.