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Warm the milk, sugar, heavy whipping cream, salt, and vanilla bean paste in a heavy-bottomed pot over medium heat just until it starts to bubble.
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While the milk mixture is heating, whisk together the egg yolks. Once the milk starts to bubble, slowly stream in about 1 cup of the milk while whisking constantly. Pour the egg yolk mixture into the pot you used to heat the milk.
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Heat the mixture over medium heat, stirring constantly, until the mixture thickens and coats the back of a spoon.
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Pour the custard through a fine mesh strainer and into a large bowl. Chill the mixture.
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Churn in ice cream maker according to manufacturer instructions. Store in freezer.