Place the unsalted butter in a large saucepan over medium heat. Let it melt slowly, stirring occasionally. Watch closely as it foams, then turns a golden brown with a nutty aroma—this usually takes about 4-5 minutes. Remove from heat immediately to prevent burning.
Add the entire package of mini marshmallows to the browned butter. Stir continuously until the marshmallows are fully melted and smooth. In a small bowl, combine pumpkin puree, pumpkin pie spice, vanilla extract, and salt. Stir this mixture into the melted marshmallows until fully incorporated and glossy.
Pour in the Rice Krispies cereal all at once. Using a spatula, fold gently but thoroughly until every crispy piece is coated with the pumpkin-marshmallow mixture. Work quickly but carefully to avoid crushing the cereal.
Lightly grease or line your 9x13-inch pan with parchment paper. Transfer the mixture to the pan and press firmly and evenly. You can use a piece of parchment paper or a flat spatula to help press down without sticking.
Let the treats cool at room temperature for about 30-40 minutes until set. Once firm, cut into squares or rectangles and serve.
