Preheat your oven to 350°F (175°C).
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and cloves.
In a separate bowl, combine the pumpkin puree, sugar, eggs, milk, and vanilla extract.
Gradually add the wet ingredients to the dry ingredients, mixing until just combined.
Spoon the batter into a greased doughnut pan, filling each mold about 3/4 full.
Bake for 15-18 minutes or until a toothpick comes out clean.
While the doughnuts cool, prepare the cheesecake filling by creaming the softened cream cheese and powdered sugar until smooth.
Add the pumpkin spice and a tablespoon of milk to the mixture, blending until creamy.
Once the doughnuts are cool, use a piping bag to inject the cheesecake filling into each doughnut hole.
Melt the butter and set aside a mixture of granulated sugar and cinnamon in a bowl.
Gently dip each doughnut into the melted butter, then roll in the cinnamon-sugar mix.