PROCEDURE: Place artichoke hearts in a large mixing bowl and mash thoroughly. Add rum, breadcrumbs, eggs, olive oil, lemon juice and garlic; mix well. Cover and refrigerate overnight. Pour Parmesan cheese in a shallow dish. Form artichoke mixture into balls, and then roll in Parmesan cheese. If desired hot, preheat oven to 400º and place balls on a baking sheet. Cook until light brown. May also be served cold and can be made in advance and frozen. Makes about 3 dozen.