Preheat the oven to 350°F (175°C). Line a standard 12-cup muffin pan with paper liners.

In a small bowl, beat the softened cream cheese and granulated sugar until completely smooth, about 1 minute.

Add the egg yolk and 1 teaspoon vanilla extract. Beat just until smooth and combined. The filling should be thick, creamy, and spoonable rather than runny. Set aside.

In a medium bowl, whisk together the flour, baking soda, cinnamon, ginger, nutmeg, cloves, and salt until evenly distributed.

In a large bowl, whisk together the pumpkin puree, brown sugar, neutral oil, 2 eggs, milk, and 1 teaspoon vanilla until smooth.

Add the dry ingredients to the pumpkin mixture: Fold gently with a spatula just until no dry flour remains. The batter should be thick and scoopable. Avoid overmixing.

Divide about half of the pumpkin batter among the 12 muffin cups, using roughly 2 tablespoons per cup. Spread it gently across the bottom.

Divide the cream cheese mixture evenly among the muffin cups, placing about 1 tablespoon in the center of each. Keep the filling away from the paper liner when possible.

Divide the remaining pumpkin batter over the cream cheese filling. The muffin cups should be about three-quarters full. Gently spread the batter so most of the filling is covered.

Sprinkle the tops lightly with coarse sparkling sugar if using.

Bake at 350°F (175°C) for 20 to 22 minutes. The muffin tops should look set and spring back lightly when touched near the edge.

Insert a toothpick into the pumpkin portion of a muffin rather than directly through the cream cheese center. It should come out with a few moist crumbs but no wet pumpkin batter.

Let the muffins cool in the pan for 10 minutes. The cream cheese centers will still be very soft when hot.

Transfer the muffins to a wire rack and cool for at least 15 more minutes before serving. The filling will become more structured as it cools.