Line a 9×9 inch pan with aluminum foil. Butter the foil or spray with cooking spray and set aside.
In a 3-quart saucepan, heat milk and sugar over medium heat. Bring to a boil, stirring occasionally with a wooden spoon.
Mix in pumpkin puree and cinnamon; bring back to a boil. Cook, stirring constantly, for 18 minutes. Remove saucepan from the heat. Allow to cool slightly, 2 to 3 minutes.
Pour white chocolate chips in a large bowl. Pour fudge mixture over white chocolate chips. Let stand 5 minutes to allow white chocolate to soften; stir until smooth. Mix in marshmallow cream, butter, and vanilla until butter is melted and mixture is smooth. Pour into prepared pan. Cool, remove from pan, and cut into squares. Store in a cool, dry place.