Preheat the oven to 350°F, and place an oven rack in the lower third position.
Line the bottom and sides of a rectangular (9 x 13-inch) baking pan with aluminum foil or parchment paper, making sure to leave an overhang on all sides. Place pan to the side.
In a large mixing bowl, using either a hand-held or stand mixer fitted with the paddle attachment, beat the butter on medium speed until it becomes smooth and creamy (about 1 minute).
Slowly add in the brown sugar and continue beating on medium-high speed until fluffy.
Add in the egg and vanilla and mix on high speed, scraping down the sides of the bowl as needed.
Add the pumpkin and mix on medium speed until completely combined.
In a separate, medium-sized bowl, whisk the flour, baking soda, cinnamon, allspice, cloves, nutmeg, ginger and salt together until completely combined.
Slowly add this dry mixture into the wet ingredients, mixing on low speed until combined. Do not overmix. The batter will be quite thick.
Spread about 2/3 of the batter evenly into the foil-lined or otherwise prepared pan. This layer will be pretty thin.
Make the cream cheese frosting. In a separate bowl, combine the 8 oz softened cream cheese, 1/2 cup granulated sugar and 2 tablespoons milk. Blend until all ingredients are completely combined and frosting is smooth and creamy.
Drop random spoonfuls of the homemade cream cheese frosting on top of the pumpkin batter in the prepared pan.
Then, drop spoonfuls of the remaining pumpkin batter on top of the cream cheese.
Using either a rubber spatula or the back of a spoon, gently swirl the two together. Both mixtures are pretty thick, so go slowly. Once swirled, carefully jiggle the pan back and forth to help the layers to settle.
Bake the bars for 30 - 35 minutes or until a toothpick inserted in the center comes out mostly clean.
Let the bars cool to room temperature on a wire rack. Once completely cooled, place the pan in the fridge for about two hours before cutting into squares to serve.