1 1/2 cups drained canned crushed pineapple in juice (from a 20-fl-oz can), reserving 1/2 cup plus 1 tablespoon juice
3/4 cup plus 2 tablespoons sugar
2 teaspoons cornstarch
1 1/4 cups whole milk
2 large egg yolks
1/4 teaspoon vanilla
1 cup chilled heavy cream
Bring pineapple, 1/2 cup reserved pineapple juice, and 1/2 cup sugar to a boil in a 2- to 3-quart heavy saucepan, stirring until sugar is dissolved. Reduce heat and simmer, stirring occasionally, until pineapple is softened, about 5 minutes. Stir together cornstarch and remaining tablespoon pineapple juice in a small bowl until cornstarch is dissolved, then add to pineapple mixture and simmer, stirring frequently, until thickened, about 1 minute.
Bring milk just to a boil in a 1 1/2- to 2-quart heavy saucepan. Whisk together yolks, remaining 1/4 cup plus 2 tablespoons sugar, and a large pinch of salt in a bowl, then add hot milk in a stream, whisking. Pour custard back into saucepan and cook over moderately low heat, stirring with a wooden spoon, until custard registers 170 to 175°F on thermometer, 2 to 3 minutes. Immediately pour custard through a very fine-mesh sieve into a bowl, then stir in pineapple mixture and vanilla and cool to room temperature, stirring occasionally. Stir in cream, then chill custard, covered, until very cold, about 4 hours.
Freeze custard in ice cream maker. Transfer ice cream to an airtight container and put in freezer to harden, at least 12 hours.