Line a 9-inch square baking pan with aluminum foil; coat with cooking spray.

Combine sugar and milk in a 3-quart saucepan over medium heat, stirring occasionally with a wooden spoon; attach a candy thermometer to the saucepan and bring mixture to a boil. Stir in pumpkin pureé and cinnamon; bring back to a boil. Cook, stirring constantly, until mixture reaches 238 degrees F (114 degrees C), about 18 minutes. Cool slightly, 5 minutes.

Place white chocolate chips in a large bowl: pour fudge mixture over top and set aside until white chocolate softens, 5 minutes. Stir until smooth. Stir in marshmallow cream, butter, and vanilla extract until butter is melted and mixture is smooth. Pour into the prepared pan.

Cool fudge, about 1 hour. Cut into squares. Store in a cool, dry place.