The process is the same for making any herbal jelly. I have used this with mint, lavender, green or purple basil. Just make an infusion of the herb, then strain the leaves out and add sugar and pectin to the infusion and boil briefly. Here's one recipe:
Do not over process in the canning stage, you can break the pectin back down again. Still not a disaster, you just end up with syrup instead of jelly.
Incidentally, the green basil jelly benefits from a little food coloring as they did here, to make it look appealing. But the purple basil jelly comes out a delightful pink color all on its own, without any food coloring.
I haven't tried them yet, but I have read about other herb jellies - sage, rosemary, lemon thyme, lemon balm...