Line a 9-by-9-inch pan with aluminum foil; 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. Stir in marshmallow cream and butter. Bring to a rolling boil and cook for 18 minutes, stirring occasionally.
Remove from heat; add vanilla and white chocolate chips; stir until creamy. Fold in walnuts if desired, saving a few to scatter on top. Pour into prepared pan. Cool, remove from pan and cut into squares. Store in refrigerator.
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