In a saucepan, heat the milk and heavy cream over medium heat until steaming, but do not boil.
In a separate bowl, whisk together the egg yolks and sugar until pale and fluffy.
Slowly pour the warm milk mixture into the egg yolk mixture, whisking constantly to prevent the eggs from curdling.
Pour the mixture back into the saucepan and cook over low heat until it thickens slightly (about 5-7 minutes), but do not boil!
Strain the mixture through a fine-mesh sieve, then stir in the rum extract, vanilla extract, and red food coloring to achieve a nice pink hue.
Let it cool to room temperature, then refrigerate for at least 4 hours, or preferably overnight, to chill thoroughly.
Pour the mixture into an ice cream maker and churn until it reaches a creamy consistency (about 20-30 minutes). During the last few minutes, stir in the diced candied fruit.
If you don't have an ice cream maker, pour the mixture into a freezer-safe container and stir with a fork or whisk every 30 minutes to prevent ice crystals from forming. Fold in the candied fruit when the ice cream starts to solidify.
Once the ice cream has reached the desired consistency, serve immediately or transfer it to an airtight container and freeze for an additional 2-3 hours to achieve the perfect firmness.
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