Special equipment: An ice cream maker and candy- or instant-read thermometer
For the ice cream: Whisk the cream, milk, sugar, vanilla and 1/2 teaspoon salt in a medium saucepan and bring to a simmer over medium heat. Beat the egg yolks in a medium bowl. Slowly whisk 1 cup of the hot cream mixture into the beaten yolks, then pour back into the saucepan,whisking, and return to medium heat. Cook, stirring constantly with a wooden spoon, until the mixture thickens, coats the spoon and reaches 180 degrees F on a thermometer, 6 to 8 minutes. Remove from the heat and strain the custard through a fine-mesh sieve into a large bowl or measuring cup; discard the solids. Stir often until the mixture cools to room temperature. Lightly press plastic wrap directly against the surface of the custard to prevent a skin from forming. Chill until cold, about 3 hours. (For faster chilling, set the bowl of custard in a bowl of ice water and stir until cold.)
For the pineapple swirl: Combine the cream, butter and 1/4 teaspoon salt in a measuring cup and set aside. Cook the sugar, corn syrup and 1 tablespoon water in a saucepan over medium heat until the sugar is dissolved. Increase the heat to medium-high and bring the mixture to a boil. Cook without stirring until it reaches a medium amber color, about 3 minutes. Remove the pan from the heat and carefully pour the cream mixture into the sugar mixture. Whisk until smooth. Stir in the crushed pineapple and any juices and return to medium heat. Cook for 10 minutes until reduced and thickened. Remove from the heat and let cool 10 minutes. Process in a food processor until pureed, then chill until ready to use.
Freeze the cold custard in an ice cream maker according to the manufacturer's directions. Transfer half of the ice cream to an 8-inch square metal pan and swirl in 1/2 cup of the pineapple with a butter knife, using circular motions to distribute pineapple throughout the cream. Add the remaining ice cream and repeat with the remaining pineapple. Cover with plastic wrap and freeze until firm, 2 to 3 hours.
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