Place the raisins in a container with a tight-fitting lid and add rum. Cover and shake to evenly coat raisins in rum, let sit at room temperature at least overnight and up to 2 days. Drain excess rum from raisins, reserving 2 tablespoons. Set aside.
Combine milk, cream, sugars, cinnamon, and salt in a medium saucepan and place over medium heat, stirring occasionally, until mixture is steaming and sugars are dissolved. Meanwhile, whisk egg yolks in a medium mixing bowl. Gradually whisk hot liquid into yolks, then scrape back into pan and cook over medium heat, stirring constantly, until mixture is thick enough to coat the back of a spoon. Strain and chill thoroughly, preferably overnight.
Add vanilla and reserved rum to base and process in ice cream machine according to manufacturer's instructions, adding raisins when almost fully churned. Remove to freezer-safe container and seal tightly. Freeze at least 24 hours before serving.
Notes:
THIS TAKES SEVERAL DAYS TO MAKE, PLAN AHEAD!
RAISINS NEED TO SOAK AT LEAST 24 HOURS
CUSTARD NEEDS TO SET UP OVERNIGHT BEFORE CHURNING
ONCE CHURNED, LET SIT IN FREEZER 24 HOURS BEFORE SERVING