Begin by whisking together all of the ingredients in a large bowl until the sugar is dissolved and the molasses has been fully incorporated. If needed, gently heat the milk over medium heat until the ingredients dissolve, then chill mixture completely. When the mixture is smooth, process in your ice cream maker according to the manufacturer's directions.
When the ice cream is done, place in a freezer-safe container and freeze for 4-6 hours. Serve with warm cookies and enjoy!