Preheat the oven to 400 degrees F (200 degrees C). Spray 2 pieces of aluminum foil with cooking spray.
Mash drained yams in a large bowl with a fork. Add ingredients in the following order, mixing well after each addition: brown sugar, cinnamon, cloves, allspice, and heavy cream. Pour mixture into two 8-inch square baking dishes. Sprinkle 1/2 of the marshmallows over each dish and cover with aluminum foil, spray-side down.
Bake in the preheated oven for 20 minutes. Remove foil and bake for an additional 5 minutes.
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