Preheat your oven to 350°F (175°C). Grease a doughnut pan with non-stick cooking spray.
In a small bowl, beat together softened cream cheese, powdered sugar, and vanilla extract until smooth. Set aside.
In a large bowl, whisk together flour, granulated sugar, baking powder, baking soda, salt, cinnamon, nutmeg, cloves, and ginger.
In another bowl, whisk together pumpkin puree, milk, sour cream, egg, melted butter, and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients, stirring until just combined. Do not overmix.
Spoon or pipe the batter into the prepared doughnut pan, filling each cavity about halfway.
Spoon a small amount of the cheesecake filling into the center of each doughnut batter-filled cavity.
Bake for 12-15 minutes, or until the edges are lightly golden and a toothpick inserted into the doughnuts comes out clean.
Allow the doughnuts to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.
In a small bowl, whisk together powdered sugar, milk, and vanilla extract until smooth to make the glaze. Adjust consistency with more milk if needed.
Dip the cooled doughnuts into the glaze, allowing any excess to drip off. Place back on the wire rack to set.
Enjoy your delicious Pumpkin Spice Cheesecake Doughnuts!