Preheat oven to 350°F. Grease a 9x13-inch cake pan or spray lightly with cooking spray.
Cake: Prepare the cake, following package directions. Stir grated pumpkin and pumpkin pie spice into the batter. Pour evenly into the prepared pan.
Bake for 30-35 minutes or until the cake is done (toothpick inserted in the center of the cake comes out clean). Cool completely in the pan on a wire rack.
Filling: Meanwhile, prepare the filling. In a small bowl (or right in the can), blend together condensed milk and cinnamon. Set aside.
When the cake is cool, using a metal skewer, a chopstick, or the handle of a wooden spoon, make holes evenly all over the cake. Pour the condensed milk mixture into the holes and all over the cake, as evenly as possible. If possible, let the cake set a half hour or so before frosting so it has a chance to absorb the filling.
Frosting: Combine cream cheese, powdered sugar, and heavy cream in a medium-sized bowl with an electric mixer until smooth and creamy.
Spread the frosting over the cake.
Refrigerate, covered, for about 2 hours before serving. If desired, garnish with additional cinnamon.
Notes
If you don’t have pumpkin pie spice, substitute 1½ teaspoons cinnamon, ½ teaspoon nutmeg, ½ teaspoon ground ginger, and ¼ teaspoon cloves.
Store airtight in the refrigerator for up to 4 days.