Chop artichokes coarsely and transfer to a small saucepan. Add garlic and olive oil. Stir briskly with a fork, cover, and cook over low heat, stirring frequently, until the garlic is cooked, about 10 minutes. Turn off heat and cover. Immediately before serving, cut cheese into small chunks while reheating the tapenade. Add cheese, whisk quickly with a fork, and serve with crackers or toast wedges and iced liquid beverages.