01 - Preheat oven to 350°F and line a 12-cup muffin tin with paper liners.
02 - Whisk together flour, sugar, baking soda, baking powder, salt, and pumpkin pie spice in a large bowl until thoroughly combined.
03 - In a separate bowl, whisk oil, eggs, pumpkin purée, milk, and vanilla extract until smooth and emulsified.
04 - Pour wet ingredients into dry ingredients and mix gently until just combined. Be careful not to overmix as this will result in tough muffins.
05 - Beat cream cheese and sugar in a medium bowl until smooth. Add egg yolk, heavy cream, cinnamon, cardamom, ginger, cloves, nutmeg, and vanilla; continue beating until creamy and well incorporated.
06 - Divide pumpkin batter among muffin cups, filling each about 2/3 full.
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 batter, creating a marbled effect.
08 - Bake for 20–22 minutes until a toothpick inserted into the muffin portion (avoiding the cheesecake center) comes out clean.
09 - Let muffins cool in the pan for 10 minutes before transferring to a wire rack to cool completely.