Combine almond paste, sugar, and vanilla in a large mixing bowl. Add egg whites (at room temperature), and beat until smooth. Chill dough at least 2 hours.
Place chilled dough in container of a cookie press fitted with a star tip. Press rosettes 2 inches apart onto lightly greased cookie sheets. Bake at 325° for 25 minutes. Remove from oven; top each cookie with a cherry half. Remove from cookie sheets, and cool on wire racks. Store in airtight containers.