In a small bowl, combine the parsley, mint, garlic, salt and 1 tablespoon olive oil. In the cavity of the artichoke from which the choke was removed, place 1 teaspoon of the herb mixture. Repeat this procedure with the remaining chokes. Arrange all chokes in a deep pan that keeps them close together, in other words, one that doesn?t give them room to fall over.
Add the wine, boiling water, remaining oil and a pinch of salt. Cover and simmer on the stovetop 1 hour.