Reserve a few mint leaves for garnish. Stir the sugar, lemon juice, and remaining mint leaves together in a medium bowl. Let stand for one hour.

Stir the milk into the lemon juice mixture, then strain the mixture through the sieve into a bowl, pressing lightly on the mint leaves; discard the mint. Add the lemon zest. The mixture will thicken slightly and may look curdled—this is okay. Pour the mixture into a shallow pan, cover, and freeze until hard, three to four hours.

Break the frozen mixture into chunks with a fork, and process in the food processor or blender until the mixture is smooth and the color has lightened. If some of the frozen chunks are stubborn, don’t be afraid to continue processing: extra processing only makes smoother, creamier sherbet.

Serve immediately as a slushy spoon drink, garnished with the reserved mint leaves, or transfer to an airtight container and refreeze until hard enough to scoop, three to four hours.

If the sherbet freezes too hard, let it soften in the fridge for 15 minutes or longer, or carefully soften it in the microwave on the defrost setting, a few seconds at a time. For the best flavor and texture, serve within two to three days.