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 well blended.
03 - In a separate bowl, whisk together oil, eggs, pumpkin purée, milk, and vanilla extract until the mixture is smooth and uniform.
04 - Pour the wet ingredients into the dry mixture and stir gently until just combined. Be careful not to overmix as this can make the muffins tough.
05 - Beat the softened cream cheese and sugar in a medium bowl until completely smooth. Add the egg yolk, heavy cream, ground cinnamon, cardamom, ginger, cloves, nutmeg, and vanilla extract. Continue beating until the filling reaches a creamy consistency.
06 - Divide the pumpkin batter among the prepared muffin cups, filling each liner 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 cheesecake mixture into the batter, creating a marbled effect.
08 - Bake for 20 to 22 minutes, or until a toothpick inserted into the muffin portion (avoiding the cheesecake center) comes out clean. The tops should be lightly golden.
09 - Let the muffins cool in the pan for 10 minutes before transferring them to a wire rack to finish cooling completely.