Abbreviated recipe for mint ice cream, but I think lemon balm would work too. Taken from Calendar Cookbook by Katie Stewart circa 1976
4oz caster sugar
1/4 pint water
1 teacup mint leaves , stripped from the stems
juice 1/2 lemon
1/2 pint double cream
Dissolve sugar in water and bring to boil.
Wash mint leaves, place in blender, then pour over hot syrup and blend briefly. Leave until quite cold then strain into a basin.
Add strained juice of 1/2 lemon and stir in cream. Whisk, and maybe add green food colouring (

).
Then freeze as usual for ice cream.
So basically the method you would use

but substituting evap. for double cream.
From memory I think it was important to strain the syrup or you ended up with yucky bits of leaf