Special equipment: An ice cream maker and a candy- or instant-read thermometer
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.)
Place an 8-inch square metal pan in the freezer to chill then freeze the cold custard in an ice cream maker according to the manufacturer's directions. Put the cookies into a resealable plastic bag and lightly crush with the smooth side of a meat mallet or the bottom of a measuring cup.
Remove chilled pan and sprinkle in half of the crumbled cookies. Top with half of the ice cream, then repeat with remaining cookies and ice cream. Working quickly, use a spoon to incorporate the cookies into the ice cream mixing from bottom to the top. Cover with plastic wrap and freeze until firm, 2 to 3 hours.
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