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To make the ice cream base: Pour the milk and cream into a saucepan set over medium-high heat and bring the mixture to a boil. Add the vanilla, remove from the heat, and let sit in the saucepan for 30 minutes.
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In a separate saucepan, beat together the egg yolks, sugar, and xanthan gum, until light and airy. Stir the warm milk and cream into the egg yolk mixture.
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Place the pan over low heat and cook the mixture, stirring, until it thickens slightly; it will register between 170°F and 180°F when measured with a digital thermometer. Remove the pan from the heat and let the custard cool to room temperature, stirring occasionally to prevent a skin from forming. Cover and refrigerate for at least 2 hours, or overnight.
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To make the marshmallow swirl: Place the egg whites and cream of tartar in the bowl of an electric mixer fitted with a whisk attachment and set aside.
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In a medium saucepan, combine the water, sugar, and corn syrup or honey. Stir to combine. Insert a candy thermometer and heat the mixture over medium-high heat. Don't stir the mixture as it cooks or it will become grainy.
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When the sugar syrup begins to form large bubbles and the thermometer reads about 225°F, begin to beat the egg whites to soft peaks (this should take about 3 to 4 minutes). By the time the egg whites are done, the sugar syrup should be at 240°F. Remove the syrup from the heat and, with the mixer running at medium-low speed, carefully pour it down the side of the bowl into the whites in a thin, steady stream.
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The whites will deflate a little at first, but continue to beat and the mixture will begin to expand. Whip for 7 to 8 minutes, until the spread is very thick and glossy. Add the vanilla and whip for 1 more minute. Pour the spread into an airtight container and store at room temperature.
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To finish the ice cream: Transfer the chilled custard to an ice cream maker and freeze according to the manufacturer's instructions. Once the ice cream begins to thicken but is still soft, fold 1 1/2 cups of the marshmallow spread into the ice cream, leaving discernible streaks throughout.
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Place the finished ice cream in a container with a tight-fitting lid and freeze for up to 2 months.