In a large saucepan over medium heat, mix pumpkin puree, pumpkin pie spice, sugar, corn syrup and evaporated milk. Stir occasionally, but be sure to mix all ingredients well.
Mixture will begin boiling. If it boils too close to the top reduce the heat slightly.
Continue cooking until mixture reaches the soft ball stage (235-245 degrees). Soft ball stage is when a small drop of syrup forms a ball when dropped into cold water, but is soft and flattens once removed from the water. When mixture reaches this stage, remove from heat.
Take the butter and grease the inside of a glass baking dish. If you want thicker fudge, use a smaller dish. Or you can use a large dish for thinner fudge.
Add the remainder of the butter and stir until mixture starts to lose it's sheen.
Pour mixture into buttered baking dish and allow to cool and set completely.