Preheat the oven to 350°F. Line a standard 12-cup muffin pan with paper liners.
Make the cream cheese filling: In a medium bowl, beat the softened cream cheese, 1/4 cup granulated sugar, egg yolk, and 1/2 teaspoon vanilla until smooth and creamy. Set aside.
Combine the dry ingredients: In a separate medium bowl, whisk together the flour, baking soda, cinnamon, ginger, nutmeg, cloves, and salt.
Combine the wet ingredients: In a large bowl, whisk together the pumpkin puree, eggs, 3/4 cup granulated sugar, brown sugar, vegetable oil, and 1 teaspoon vanilla until smooth.
Make the batter: Add the dry ingredients to the pumpkin mixture. Gently fold with a rubber spatula just until no dry streaks of flour remain. Do not overmix.
Fill the muffin cups: Add about 2 tablespoons of pumpkin batter to each muffin cup. Spoon approximately 1 tablespoon of cream cheese filling into the center, keeping it away from the sides. Divide the remaining pumpkin batter among the cups, placing it around and partially over the cream cheese. A little filling can remain visible on top.
Bake at 350°F for 22–26 minutes, or until the pumpkin portion of the muffins is risen and set. Insert a toothpick into the pumpkin crumb near the edge rather than through the cream cheese center. It should come out clean or with a few moist crumbs.
Let the muffins cool in the pan for about 10 minutes, then transfer them to a wire rack. Cool completely to allow the cream cheese centers to set.