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Place the half-and-half and the heavy cream into a medium saucepan, over medium heat.
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Bring the mixture just to a simmer, stirring occasionally, and remove from the heat.
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In a medium mixing bowl whisk the egg yolks until they lighten in color.
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Gradually add the sugar and whisk to combine.
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Temper the cream mixture into the eggs and sugar by gradually adding small amounts, until about a third of the cream mixture has been added.
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Pour in the remainder and return the entire mixture to the saucepan and place over low heat.
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Continue to cook, stirring frequently, until the mixture thickens slightly and coats the back of a spoon and reaches 170 to 175 degrees F. Pour the mixture into a container and allow to sit at room temperature for 30 minutes.
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Stir in the vanilla extract.
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Place the mixture into the refrigerator and once it is cool enough not to form condensation on the lid, cover and store for 4 to 8 hours or until the temperature reaches 40 degrees F or below.
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Pour into an ice cream maker and process according to the manufacturer's directions. This should take approximately 25 to 35 minutes.
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Serve as is for soft serve or freeze for another 3 to 4 hours to allow the ice cream to harden.