Drop pumpkin puree onto a couple layers of paper towels. Fold the towel over and squeeze out the moisture. Scrape the the puree onto a dry part of the towel and repeat once or twice more, until most of the moisture has been removed and you can pick up the puree with your fingers.

In a medium pan, combine prepared puree, butter, cinnamon, nutmeg, ground cloves, and ginger. Heat over medium heat until butter is melted and whisk until mostly combined. Add 1 1/2 cup of the marshmallows and use a heat-proof rubber spatula to stir until mostly melted and combined.

Remove from heat and stir in Rice Krispies and remaining 1/2 cup of marshmallows. Stir just until everything is well-mixed (some of the marshmallows will not completely melt). Transfer to your greased dish or drop onto lightly greased parchment paper. Cool completely, about 20 minutes.

In a small microwave-safe bowl, heat milk for 10 to 20 seconds until steaming. Add chopped white chocolate and stir until melted. Drizzle over the rice krispies treats with a spoon or transfer to a disposable plastic bag and snip off one of the corners to "pipe" your chocolate. Allow another 10 minutes of cooling time before eating.

Store in an air-tight container at room temperature.