01 - Preheat oven to 350°F and line a 12-cup muffin tin with paper liners.
02 - In a large bowl, whisk together flour, sugar, baking soda, baking powder, salt, and pumpkin pie spice until well combined.
03 - In a separate bowl, whisk together oil, eggs, pumpkin purée, milk, and vanilla extract until smooth and homogeneous.
04 - Pour the wet mixture into the dry ingredients and fold gently until just combined. Take care not to overmix as this can result in dense muffins.
05 - Beat the cream cheese and sugar in a medium bowl until smooth and creamy. Add egg yolk, heavy cream, cinnamon, cardamom, ginger, cloves, nutmeg, and vanilla; continue beating until fully incorporated and silky.
06 - Distribute the pumpkin batter among the prepared muffin cups, filling each about 2/3 full to allow room for rising and the cheesecake swirl.
07 - Drop approximately 1 tablespoon of chai cheesecake filling onto the center of each muffin. Use a toothpick to gently swirl the cheesecake layer into the pumpkin batter, creating a marbled effect.
08 - Bake for 20 to 22 minutes, or until a toothpick inserted into the pumpkin portion (avoiding the cheesecake center) comes out clean. The tops should be lightly golden and spring back when touched.
09 - Allow the muffins to cool in the pan for 10 minutes before transferring to a wire rack. Cool completely before serving to allow the cheesecake filling to set properly.