Our version of the traditional Indian dessert is this elegant ice-cream cake.
In a small saucepan over medium heat, warm the coconut milk and cardamom pods until milk just reaches a boil. Stir well, cover, and set aside to infuse for 30 minutes
Heat oven to 350 degrees. Place pistachios on a baking sheet; toast until aromatic, about 8 minutes. While warm, transfer nuts to a clean kitchen towel; rub to remove the brown skins. Set nuts aside. (If using whole blanched almonds, simply toast, and set aside.)
Place the condensed milk, pistachio nuts, and almond slivers in a food processor. Process until well blended and the nuts are finely chopped. Strain the coconut milk into the nut mixture. Pulse until just combined. Transfer the mixture to a large bowl.
In an electric mixer, whip the heavy cream to soft peaks. Gently whisk the cream into the coconut mixture.
Strain 1 cup of the mixture into the bottom of a 5-cup oval pudding mold. Transfer mold to freezer, and let chill until firm, 1 hour to 1 1/4 hours. (Poke the mixture lightly with your finger to test for firmness.) Stir well, and pour 1 1/2 cups of the remaining coconut mixture (not strained) over the frozen mixture, return to freezer, and chill until firm, about 1 1/2 hours.
Puree mango; it should yield about 1/2 cup. Combine puree and corn syrup in a bowl. Pour mango mixture over the frozen mixture; freeze until firm, 30 to 40 minutes. Stir well; pour remaining coconut mixture over frozen mango layer until mold is full. Cover with plastic wrap; freeze overnight.
To unmold cake, remove plastic wrap; place the mold, metal-side up, on a serving platter. Wet a kitchen towel with very hot water; wring out. Place the towel over the mold, and press into the mold, being careful to press the warm towel into any curves or flutes of the mold. Repeat this step as needed, until kulfi slips out onto the platter. Return cake to freezer on platter until firm again, at least half an hour. Cake may be made up to this point 1 day ahead. To serve, place in refrigerator about 20 minutes, until soft enough to cut with a serrated or slicing knife. Cut mangoes into wedges, if using.