In a food processor, puree 12 oz mango slices until smooth. Strain the puree through a fine sieve. Add 2 tablespoons rum to the puree and refrigerate it while you make the ice cream base.
Heat 16 oz heavy cream in a small saucepan over medium high heat until scalding hot.
While the cream heats up, whisk together 5 egg yolks and 6 oz granulated sugar in a small bowl.
Once the cream mixture is scalding hot, pour it into the bowl with the yolks and whisk to combine
Return the entire mixture to the saucepan and heat over medium low heat, stirring constantly. Cook the custard until it thickens enough to coat the back of a spatula or wooden spoon. Do not allow it to come to a full boil. Remove from the heat and pour back into the bowl from the yolks. Add the cold mango puree to the custard and stir to combine.
Cover the bowl and chill until very cold. At least 4-5 hours or over night.
Freeze according to the directions for your ice cream machine.
When the ice cream is ready, scoop it into a container and smooth to an even layer. Lay a piece of plastic wrap directly on the surface of the ice cream, cover tightly and freeze until firm.
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