Combine the milk (I used skim because I had some on hand, but you can use any type you like) and basil in the blender and blend on high until the basil is very finely ground up, about 1 minute.
Whisk the basil milk with the salt, sugar, and egg yolks in the top of a double boiler and cook over simmering water until it thickens slightly, about 10 minutes, stirring often.
Remove from heat and add the extracts, lemon zest and juice, and cream, cover, and refrigerate until well chilled. Process in an ice cream machine according to the manufacturer's directions, and then freeze in a covered container.
Recipe by Cooking With MicheleĀ® at https://cookingwithmichele.com/2016/09/lemon-basil-gelato/