1 cup cream
2 cups milk
4 egg yolks
3/4 cup sugar, divided
1/3 cup chopped fresh basil
Pinch of salt
Heat the cream, milk, basil, and 1/4 cup sugar to boiling in the microwave. Strain out the basil and place it in a blender or food processor along with 1/4 cup of the liquid. Puree until smooth, then stir back into the dairy mixture.
Whisk the egg yolks and remaining 1/2 cup of sugar together until smooth and lighter in color. Whisking constantly, drizzle the hot milk/cream/sugar/basil mixture into the egg/sugar. Once combined, transfer the mixture to a pot and place over medium-low heat. Stir or whisk constantly until it reaches 170F or has thickened to the nappe stage (coats the back of a spoon), then remove promptly from the heat. Strain through a fine-mesh sieve to remove any curdled egg bits.
(The method I use to avoid all chances of curdling is to mix the eggs and sugar in a large metal bowl, and then after mixing in the milk/cream, place the bowl over a pot of simmering water and whisking. This longer, but you won’t have to strain it afterwards. Also, you can be somewhat less paranoid about the constant whisking of the mixture- this cooking method is gentler than direct heat.)
Stir in the salt. Cool for at least four hours (or overnight).
Freeze in an ice cream maker, following the manufacturer’s instructions. Transfer to freezer to let harden.