In a medium saucepan, whisk together all the ingredients, minus the candied ginger, and bring to a simmer over medium heat. Let cool completely, then refrigerate overnight. Make sure you freeze the bowl of an ice cream maker during this time.
The next day, strain the base into the bowl of the ice cream maker and churn according to the manufacturer's directions. Scrape into a shallow dish and freeze for at least 4 hours. Scoop the ice cream into bowls and drizzle with honey. Garnish with chopped candied ginger, then serve.