Heat the milk and cream until boiling, then remove from heat. Add basil leaves and vanilla and allow to infuse for 20 minutes. Just before the 20 minutes has elapsed, beat sugar and eggs in a blender. Pour the cream mixture through a sieve into the blender, discarding the basil leaves. Blend until thoroughly combined. Refrigerate until chilled—at least 4 hours.

Pour into ice cream maker and process according to directions. In my ice cream maker, the ice cream is generally quite soft when first finished, so I leave it for at least an hour in the freezer before enjoying. If you do not have an ice cream maker, you can pour the mixture into a freezer-safe shallow pan, place it in the freezer, and remove it every 20 minutes to beat with an electric mixer for 5 minutes each time. Continue the process over the course of several hours, until frozen and rich and creamy. The texture will not be quite the same as when you use an ice cream maker, and you may have some trial and error, but hey, since in the end you get ice cream, I think you’ll be happy.

If you fancy my version of a grown-up Dixie Cup presentation, spoon ice cream into individual ramekins and smooth the top with a palette knife or offset spatula. When fully set, garnish each ramekin with an individual basil leaf and freeze for an additional 5 minutes.