Line a 9-inch round metal cake pan with plastic wrap; place in freezer.

In a medium saucepan, combine cream, milk, corn syrup, ¼ cup (50 grams) sugar, vanilla bean paste, and salt. Heat over medium-high heat, stirring occasionally, until a candy thermometer registers 170°F (77°C). Remove from heat. Stir in maraschino cherries and juice.

In a medium bowl, whisk together egg yolks and remaining ¼ cup (50 grams) sugar. Add 1 cup hot cream mixture to egg mixture, whisking constantly. Add egg mixture to remaining hot cream mixture in pan, whisking to combine. Cook over medium-low heat until mixture is thickened and a candy thermometer registers 180°F (82°C), 7 to 10 minutes. Immediately pour custard into a large bowl, and let cool until no longer steaming, 10 to 20 minutes.

Transfer 1 cup mixture to a small jar with a tight-fitting lid. Place remaining mixture in a large jar with a tight-fitting lid. Refrigerate large jar and freeze small jar for at least 6 hours or up to 24 hours.

Remove frozen base from freezer, and let stand at room temperature for 10 minutes. Scrape frozen base into a large bowl; add refrigerated base, and stir occasionally until frozen base is dissolved. Transfer mixture to an ice cream maker, and churn until soft serve consistency, about 20 minutes.

Transfer ice cream to prepared pan, and press plastic wrap directly onto surface. Freeze overnight. Remove from freezer, and let stand at room temperature for 10 minutes to soften.