To prepare bourbon cherries, cook cherries, sugar and water in a small saucepan over medium heat, stirring occasionally, until syrupy, about 10 minutes. Remove from heat and stir in bourbon. Let cool to room temperature.
In a medium saucepan, combine milk, heavy cream and 1/2 cup sugar and salt. Bring mixture to simmer, until sugar is dissolved. Remove from heat and set aside.
Whisk egg yolks and remaining sugar in a medium bowl until pale, about 2 minutes. Gradually whisk in half of the warm cream mixture, mix until blended. Stir yolk mixture into the remaining cream mixture. Cook over medium heat, stirring constantly, until thick enough to coat a wooden spoon, about 2 to 3 minutes. Mix in vanilla.
Strain custard into another medium bowl, let cool over a bowl of ice water, or chill in the refrigerator, stirring occasionally, until it becomes cool.
Process custard in an ice cream maker according to manufacturer’s instructions. Few minutes before it’s done processing, add the cherries, and drizzle in the melted dark chocolate, while the machine is running.
Transfer to an airtight container, cover and freeze until firm, at least 4 hours.