Preheat Oven: Preheat to 350°F (175°C). Line a 12-cup muffin tin with paper liners.
Mix Dry Ingredients: In a large bowl, whisk together flour, sugar, baking powder, baking soda, salt, cinnamon, and nutmeg.
Combine Wet Ingredients: In another bowl, mix milk, oil, pumpkin, eggs, and vanilla.
Combine Mixtures: Gently fold the wet ingredients into the dry ingredients until just combined.
Prepare Cream Cheese Swirl: In a medium bowl, beat cream cheese with sugar, egg yolk, and vanilla until smooth.
Fill Muffin Cups: Spoon batter into muffin cups, filling each about ¾ full. Drop small spoonfuls of cream cheese mixture onto the batter. Use a toothpick or knife to swirl the cream cheese into the batter.
Bake: Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean.
Cool: Allow muffins to cool in the pan for 5 minutes before transferring to a wire rack to cool completely.