Preheat oven to 350° F. Prepare a 9x13 baking dish with cooking spray and set aside.
In a large mixing bowl, combine the cake mix, pumpkin puree, water, oil, eggs, and vanilla. Mix with a hand mixer for about 2 minutes or until smooth.
Pour the cake mixture into the prepared baking dish, and bake for 25-30 minutes or until a toothpick inserted in the center comes out clean. Set aside to cool for 15 minutes.
Once cooled, taking a wooden spoon (or dowel), poke holes in the cake.
In a small bowl, mix the 1 cup of sweetened condensed milk with the pumpkin pie spice, and pour the mixture into the holes; cover the cake and refrigerate 2 hours.
Make the cream cheese frosting:
In the bowl of a stand mixer or a large mixing bowl using a handheld mixer, beat the cream cheese until smooth. Add the butter and beat for another 30 seconds to 1 minute until well combined and smooth.
Add in the powdered sugar and vanilla and beat until smooth.
Remove the cake from the refrigerator and spread the cream cheese frosting evenly over the cake. Sprinkle the cake with fresh grated nutmeg for garnish (optional). Slice into 12 pieces and serve!