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Put corn and half and half in a food processor and process until smooth. Pour into a fine mesh strainer and use a rubber spatula to make sure you get all the liquid out; discard solids. Transfer to a large pan and add milk, sugar, salt, and egg yolk; whisk to combine.
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Heat over medium heat, whisking the entire time, until it's thickened enough to coat the back of a wooden spoon. Remove from heat and let cool to room temp. Once cool, transfer to a bowl and refrigerate until chilled.
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While that's chilling, heat the milk and caramel candies over super low heat, stirring until the caramels have melted and the mixture is smooth. Let cool slightly.
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Once ice cream mixture is chilled, pour into your ice cream maker and freeze according to the instructions for your machine. Transfer ⅓ of the ice cream into your freezer-safe container. Spoon ½ of the caramel over that. Repeat the layers, ending with ice cream. Freeze at least 2 hours before serving.
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Top with caramel corn is desired.