Preheat your oven to 375°F (190°C). Line a standard 12-cup muffin tin with paper liners or grease them thoroughly with non-stick cooking spray to ensure easy removal.
In a large mixing bowl, whisk together the all-purpose flour, 1 cup of granulated sugar, brown sugar, baking soda, salt, and pumpkin pie spice. Ensure there are no large lumps of brown sugar left in the mix.
In a separate medium bowl, whisk together the pumpkin puree, vegetable oil, two eggs, and 1 teaspoon of vanilla extract until the mixture is smooth and well combined.
Gently fold the wet pumpkin mixture into the dry ingredients using a spatula. Mix only until just combined; overmixing can lead to a tough muffin texture. Set this batter aside.
In a small bowl, beat the softened cream cheese, ¼ cup of sugar, egg yolk, and ½ teaspoon of vanilla extract. Use an electric mixer or a sturdy whisk to ensure the filling is completely smooth and creamy.
Spoon the pumpkin batter into the muffin liners, filling them about ¾ full. Place a dollop (about one tablespoon) of the cream cheese mixture onto the center of each muffin. Use a toothpick or a small knife to gently swirl the cream cheese into the batter. Bake for 18-22 minutes, or until a toothpick inserted into the cake part comes out clean. Allow them to cool in the pan for 5 minutes before moving to a wire rack.