In a medium saucepan, combine cream, milk, and honey over medium heat. Heat until steaming but not boiling, stirring occasionally.
Remove the pan from the heat and whisk in the goat cheese until it is completely melted into the cream mixture and no lumps remain. Transfer the mixture to a 2 quart or larger covered storage container and refrigerate until completely cold, a few hours up to overnight.
Churn the ice cream in your ice cream maker according to manufacturer's directions. Transfer the ice cream to a freezer safe container and store in the freezer until firm, at least two hours. Homemade ice cream is best enjoyed within a few days.