1. Wash and trim the artichokes, removing the thin inner leaves and fuzzy choke.
2. Melt the butter in a large skillet. Add the garlic and anchovies, then stir over medium heat for 30 seconds. Stir in the bread crumbs and blend well so that the crumbs absorb the melted butter. Remove from the heat and mix in the mint, parsley, salt, and cayenne.
3. Preheat the oven to 375°. Spread apart the leaves of each artichoke and stuff with the bread crumb mixture. Spoon some of the stuffing into the center cavity. Pour the wine and olive oil into a shallow baking dish. Set the artichokes in the liquid and cover the dish with aluminum foil. Bake for 30 minutes. Uncover and continue baking for an additional 15 minutes.
4. Serve the artichokes hot or at room temperature.