In a medium saucepan, heat the milk over very low heat until steamy but not boiling. Turn off the heat, add the rosemary and steep it in the milk for 30 minutes.

Meanwhile, whisk together the cream and the sugar. Remove the rosemary from the milk mixture and discard the rosemary; add the scented milk to the cream/sugar mixture and stir. Slowly stir in the cherries.

Chill the cherry-cream mixture for three to four hours. Then process the mixture according to your ice cream maker manufacturer's instructions.