Heat the oven to 375°F. Line 18 standard muffin cups with paper liners and set aside.

In a medium bowl, whisk the flour, pumpkin pie spice, baking soda, and salt until well combined.

In a large bowl, whisk the pumpkin puree with the granulated sugar and brown sugar until smooth. Beat in the eggs, neutral oil, and vanilla. Add the dry mixture and stir just until no streaks of flour remain. Divide the batter among the prepared muffin cups, filling each about three quarters full.

In a separate medium bowl, beat the softened cream cheese until silky. Add the remaining sugar, egg yolk, and vanilla, and beat until the swirl mixture is smooth and well combined.

Spoon about 1 tablespoon of the cream cheese mixture onto the center of each muffin. Use a toothpick to gently swirl it into the batter; the tops will look messy before baking, but they will bake up beautifully. If preferred, simply drop the mixture in the center without swirling.

Bake for 18 to 20 minutes, until a toothpick inserted into the pumpkin portion comes out clean with just a few moist crumbs. Cool in the pan for 10 minutes, then serve warm or let cool completely on a wire rack.