Place cream, molasses, sugar, vanilla, and spices in a large bowl. Whip until cream begins to thicken. Stop before it reaches a thickness that can be dolloped.Gradually beat in milk and mix well to combine.Pour mixture into an ice cream maker and churn according to manufacturer's instructions. This usually takes about 15–20 minutes for me. During the last minute or so of churning, add the gingerbread cookie chunks.Transfer to a freezer-safe container and freeze until solid, about 2 hours.