1. Combine the basil, ½ teaspoon of the coriander or 1 teaspoon of the parsley, cayenne pepper, salt and garlic in a large bowl and mash to a paste with the back of a large wooden spoon.
2. Combine the jam and vinegar in a 1-quart enameled or stainless-steel sauce-pan and, stirring constantly, bring to a boil over high heat and continue to boil until the jam has dissolved.
3. With the back of a wooden spoon, rub the mixture through a fine sieve set over a small bowl. Beat it into the herb-and-garlic paste, a tablespoon at a time.
4. Add the beans and toss together gently until the beans are coated with the sauce. Taste for seasoning. Let the beans rest at room temperature for 2 or 3 hours, or cover with plastic wrap and refrigerate overnight.
5. Serve the Lobio Ttkemali at room temperature, sprinkled with the remaining chopped coriander or parsley.