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 thoroughly combined.
03 - In a separate bowl, whisk together oil, eggs, pumpkin purée, milk, and vanilla extract until smooth and well incorporated.
04 - Add the wet ingredients to the dry ingredients and fold until just combined. Avoid overmixing to prevent tough 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; beat until fully incorporated and silky.
06 - Divide the pumpkin muffin batter among the prepared liners, filling each about two-thirds full.
07 - Drop approximately 1 tablespoon of chai cheesecake filling onto the center of each muffin. Use a toothpick to gently swirl the filling into the batter, creating a marble effect.
08 - Bake for 20 to 22 minutes, or until a toothpick inserted into the muffin portion (avoiding the cheesecake center) comes out clean.
09 - Let the muffins cool in the pan for 10 minutes before transferring to a wire rack to cool completely.