Preheat your oven to 350 degrees Fahrenheit and line a 12-cup muffin tin with paper liners.
In a large bowl, whisk together the pumpkin puree, eggs, sugar, and vegetable oil until well combined.
Add the flour, baking soda, salt, cinnamon, cloves, and ginger and mix with a rubber spatula just until no streaks of flour remain. Set the batter aside.
Combine the cream cheese, 1/2 egg, and sugar in a medium bowl with a wire whisk until the mixture is creamy and smooth. Set aside.
Portion out the pumpkin batter into the 12 muffin cups, filling each one about 2/3 full.
Add one tablespoon or so of the cheesecake mixture to the top of each and use a toothpick to swirl the cheesecake mixture into the pumpkin batter.
Bake the muffins at 350 degrees Fahrenheit for about 20 minutes, or until the muffins pass the toothpick test (insert a toothpick and if it comes out clean, they're done!).
Allow the muffins to cool in their pans for about 10 minutes before removing them to a wire rack to cool completely.
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Notes
These muffins keep at room temperature in an airtight container for about 2 days.