Preheat oven to 350 degrees Grease a 9-inch pie dish with cooking spray.
Unroll crescent rolls and smooth the perforation lines until sealed. Spread pumpkin puree evenly onto crescent roll dough. Sprinkle with brown sugar and pumpkin pie spice.
Bake for approximately 20-25 minutes, until risen and browned. Let cool before adding frosting.
For the frosting, add softened cream cheese, powdered sugar, melted butter, vanilla extract, and milk to a medium mixing bowl. Using a hand mixer, mix until whipped and smooth.
Spread frosting onto the tops of the pumpkin cinnamon rolls and serve.