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Infuse the milk/cream:
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1. In a medium heavy saucepan, stir together the cream, milk, half of the sugar (1/4 cup), and salt.
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2. Put the pan over medium high heat. Add the basil leaves to the pan. When the milk just begins to bubble around the edges, remove from heat and cover the pan. Let steep for about 20 minutes, or until a sweet basil flavor has infused into the milk/cream. (Taste it to monitor the progress - beware, it will become bitter if oversteeped.) Don't be alarmed if the basil turns black, it won't affect the color or flavor of the ice cream.
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Make the base:
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1. In a medium heatproof bowl, whisk the yolks just to break them up, and then whisk in the remaining sugar (1/4 cup). Set aside.
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2. Uncover the cream mixture and put the pan over medium high heat. When the mixture approaches a bare simmer, reduce the heat to medium.
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3. Carefully scoop out about 1/2 cup of the hot cream mixture and, whisking the eggs constantly, add the cream to the egg bowl. Repeat, adding another 1/2 cup of the hot cream to the egg bowl. Then, return to the pan of cream on the stove and, using a heatproof spatula, stir the cream as you slowly pour the egg and cream mixture from the bowl into the pan.
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4. Continue to cook the mixture carefully over medium heat, stirring constantly until the mixture is thickened, coats the back of a spatula and leaves a clear mark when you run your finger across it, 1-2 minutes longer.
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5. Strain the base through a fine-mesh strainer and into a clean container. Set into an ice bath, wash your spatula, and stir occasionally until the base is cool. Cover with plastic wrap and refrigerate the base for at least 2 hours or overnight. Freeze the ice cream
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6. Freeze in your ice cream machine according to the manufacturer's instructions. While the ice cream is churning, put the container you'll use to store the ice cream into the freezer. Enjoy right away or for a firmer ice cream, freeze for at least 4 hours.
