The night before you plan to make the ice cream, freeze the bowl of your ice cream maker.
Place pitted cherries, 1/4 cup honey, and vanilla in a medium sauce pan and bring to a simmer over medium heat. Reduce heat and continue to simmer as the fruit begins to release its juice.
Use a potato masher or fork to mash the cherries a bit, so that they're slightly broken down. Simmer for 10-15 minutes more, until some of the liquid evaporates and the fruit is tender but not falling apart. You'll have just about 1 1/4 cup of fruit when it's done.
Remove cherries from heat, transfer to a bowl, and chill in the fridge.
In a large stock pot over low heat, whisk the goat cheese into the buttermilk, cream, additional 1/4 cup honey, and lemon zest. Continue to whisk until smooth, then remove from heat. Let cool for 10 minutes.
In a small bowl, whisk the egg yolks with 1/2 cup of the ice cream mixture, then gradually whisk the egg yolk mixture back into the pan. Return to the stove, and cook over low heat, stirring continuously, until the custard reaches 170ºF, 20 to 25 minutes, or until it thickens slightly and coats the back of a spoon. Remove from heat.
Transfer the custard to a bowl, stir in 1/2 cup of the crushed cherries, cover, and chill completely in fridge.
Once the custard is fully chilled, freeze it in the ice cream maker according to the manufacturer's instructions. Transfer to a freezer safe container and swirl in the remaining cherries with a spoon. Cover, and freeze for at least 4-6 hours before eating.