Preheat oven to 425°F (220°C). Line a standard 12-cup muffin tin with paper liners.

In a medium bowl, beat softened cream cheese, granulated sugar, egg yolk, and vanilla extract with an electric mixer until completely smooth, silky, and lump-free.

In another bowl, whisk together flour, baking powder, baking soda, pumpkin pie spice, and salt.

In a large mixing bowl, whisk pumpkin puree, granulated sugar, dark brown sugar, oil, eggs, milk, and vanilla until smooth and thoroughly emulsified.

Fold dry flour mixture into wet pumpkin mixture with a rubber spatula just until no dry flour streaks remain. Do not overmix!

Divide half the pumpkin batter evenly among 12 muffin cups. Dollop 1 tablespoon of cream cheese mixture into the center of each. Cover with remaining pumpkin batter. Top each muffin with a final teaspoon of cream cheese, and use a toothpick to swirl into pretty marble patterns.

Sprinkle tops generously with sparkling turbinado sugar.

Bake at 425°F (220°C) for exactly 5 minutes (the initial burst of high heat creates dramatic, tall bakery domes).

Without opening oven door, reduce heat to 350°F (175°C) and bake for an additional 15 to 17 minutes until muffin tops spring back and a toothpick inserted in cake part comes out clean.

Cool in pan for 10 minutes, then transfer to a wire cooling rack to cool completely. Serve slightly warm or chilled.