In a large bowl, or standup mixer, cream butter and sugar until light and fluffy. Beat in eggs and orange peel. Combine the flour, baking powder and salt in another bowl; add to creamed mixture just until blended. Mix in vanilla. Fold in currants.
Fill greased muffin cups or paper lined muffin cups two thirds full. Bake in preheated over at 350° for 20 to 25 minutes or until toothpick inserted near the center comes out clean. Cool for 5 minutes before removing from pan to a wire rack. You can eat these warm or cold and also you can dust them with confectioners' sugar if you want to.