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Place all ingredients in a sauce pan excluding the rum. Heat slowly and whisk the mixture the entire time. When very hot to the touch add the rum. Begin to gently simmer and keep it low.
Stir for 2 minutes. Remove from heat source and let sit for about 10 minutes.
Pour into a glass dish. Refrigerate for at least 3 hours to chill completely.
Stir. Place in ice cream maker and follow your ice cream maker’s directions. Leftovers can be covered and stored and will not harden. You now have soft serve coffee ice cream at any time you desire.