Place the half-and-half, basil, sugar, salt and egg yolks in a blender. Blend until completely smooth.
Transfer the mixture to a double boiler, and heat, stirring constantly, until the eggs just begin to thicken and the sugar has dissolved. Remove from the heat and strain through a fine-mesh sieve into a metal bowl. Set the bowl in an ice water bath to rapidly chill.
Churn in an ice cream machine according to manufacturer's instructions. Freeze until ready to use.
Recipe courtesy of Tyler Florence