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1
Combine sugar, corn syrup, cream of tartar, and 1/4 cup water in a medium saucepan. Stir over medium-low heat until sugar dissolves. Increase heat and cook without stirring, occasionally swirling pan and brushing down sides with a wet pastry brush, until dark amber in color, about 7 minutes.
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2
Remove from heat; immediately add butter and stir until melted. Slowly add cream (mixture will bubble vigorously). Add vanilla and salt; whisk until smooth.
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3
Can be made 1 month ahead. Let cool completely. Cover sauce and chill. Rewarm slightly before using.
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4
Set a strainer over a large bowl; set aside. Place popcorn in another large bowl. Drizzle butter over and sprinkle with 1/2 teaspoon salt; toss to coat. Add milk and cream; cover and steep for 10 minutes. Stir in corn syrup and 1 tablespoon sugar. Working in batches, puree popcorn mixture in a blender until smooth. Transfer to a large saucepan and bring to a simmer over medium heat.
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5
Using an electric mixer, beat yolks, remaining 4 tablespoons sugar, and remaining 1/2 teaspoon salt in a large bowl until thick ribbons form. Gradually whisk hot popcorn mixture into yolk mixture. Return to saucepan and cook over medium-low heat, stirring constantly with a wooden spoon, until custard is slightly thickened, your finger leaves a path when drawn across the back of a spoon, and an instant-read thermometer registers 175u00b0F, 3-4 minutes. Pour through strainer. Cover and chill overnight.
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6
Process in an ice cream maker according to manufacturer's instructions. Transfer to a container, cover, and freeze. DO AHEAD:
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7
Stir both chocolates in a medium metal bowl set over a saucepan of simmering water until melted and smooth. Set aside. Place peanut brittle in a food processor and pulse until finely ground. Add peanut butter and melted chocolate. Pulse until combined. Spread out on a baking sheet. Chill for at least 4 hours. DO AHEAD:
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8
Spoon some caramel sauce into tall, decorative glasses or serving bowls. Add 2 scoops buttered-popcorn ice cream. Drizzle more caramel sauce over. Sprinkle some halvah over. Top with a spoonful of whipped cream. Garnish sundae with peanuts and buttered popcorn.
