Step 1: Prepare the cheesecake filling: In a medium bowl, beat softened cream cheese with 1/4 cup granulated sugar, 1/2 tsp vanilla extract, and 1 egg yolk until smooth and creamy. Set aside.
Step 2: Prepare the cookie dough: In a large bowl, cream together softened butter, 1 cup granulated sugar, and brown sugar until light and fluffy.
Step 3: Beat in the large egg and pumpkin puree until well combined.
Step 4: In a separate bowl, whisk together the flour, baking soda, cinnamon, ginger, nutmeg, cloves, and salt.
Step 5: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Step 6: Drop rounded tablespoons of pumpkin cookie dough onto baking sheets lined with parchment paper, leaving about 2 inches between cookies. Dollop about 1 teaspoon of the cheesecake mixture onto the center of each pumpkin cookie dough mound. Gently swirl the cheesecake into the pumpkin dough with a toothpick or small knife.
Step 7: Bake in a preheated oven at 375°F (190°C) for 12-15 minutes, or until the edges are set and the cheesecake swirl is lightly golden. The centers may still look soft.
Step 8: Remove from the oven and let cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely. Store leftover cookies in an airtight container in the refrigerator.