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1
Preheat oven to 300 degrees F (150 degrees C). Line a 9x13-inch baking pan with parchment paper; coat with cooking spray.
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2
Mix 3/4 cup white sugar, egg yolks, egg, vanilla extract, 1 teaspoon cardamom, and 1/2 teaspoon salt together in the bowl of a stand mixer fitted with the paddle attachment; mix on low speed until well combined.
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3
Heat cream in a small saucepan over medium heat, stirring often, until it begins to bubble, about 5 minutes; remove from heat. Add cream to the egg mixture slowly, mixing on low speed. Pour custard into the prepared baking dish.
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4
Set the baking pan into a roasting pan; carefully pour enough boiling water into the roasting pan to come halfway up the sides of the baking pan.
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5
Bake in the preheated oven until the custard is set when gently shaken, 45 to 50 minutes.
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6
Remove baking pan from roasting pan. Cool to room temperature, about 30 minutes. Freeze until firm, at least 1 hour.
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7
Melt butter in a skillet over medium heat. Add brown sugar, salt, 1/4 teaspoon cardamom, and cinnamon; stir to combine. Add frozen pumpkin and simmer, stirring often, until reduced, about 8 minutes. Cool candied pumpkin to room temperature, about 10 minutes.
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8
Cut custard into 18 squares using a pizza cutter or sharp knife. Place 1 custard square in a serving dish, add a layer of candied pumpkin, and top with another square. Sprinkle each with 1 tablespoon of sugar. Use a kitchen torch to flame tops until deeply caramelized and a crunchy layer has formed.
