Preheat your oven to 350 degrees Fahrenheit (175 degrees Celsius) 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 (175 degrees Celsius) 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.