In a large pot, melt the butter over medium heat. Reduce the heat to low, then remove 1 tablespoon of the butter and pour it into an 11x7-inch pan, brushing it edge to edge to grease the pan.

Add the pumpkin puree to the melted butter, stirring until smooth and well-incorporated. Cook on low, stirring constantly, for about 1 minute until the pumpkin is hot.

Stir in the marshmallows and cook on low, stirring constantly, until fully melted. Remove from heat and mix in the pumpkin pie spice and vanilla extract.

In a large mixing bowl, combine the Rice Krispies with the pumpkin marshmallow mixture. Quickly mix to evenly coat the cereal before it starts to set, then scoop into the prepared 11x7-inch pan. Use a buttered spatula to spread it out evenly.

Chill the Rice Krispies treats in the refrigerator for 1 hour, or until fully set.

Remove the Rice Krispies treats from the pan and place on a cutting board. Use a sharp knife to cut into 12 squares.

Melt the white chocolate according to package directions. Use a spoon to drizzle the melted chocolate over the treats. For quicker setting, refrigerate the treats, or allow them to set at room temperature (about 30 minutes).