1Dissolve yeast in apple juice in large bowl; let stand 1 minute. Mix in 2 cups of the flour, 1/3 cup sugar, the salt, 1/4 cup butter and the egg; beat vigorously with wire whisk until well blended. Stir in enough remaining flour to make dough easy to handle.
2Place dough on lightly floured surface; gently roll in flour to coat. Knead about 3 minutes or until smooth and springy. Place dough in large bowl greased with shortening, turning dough to grease all sides. (Dough can be refrigerated at this point no longer than 24 hours.) Cover bowl tightly with plastic wrap and let rise in warm place 60 to 70 minutes or until almost double. (Dough is ready if indentation remains when touched.)
3Grease 12 medium muffin cups, 2 1/2x1 1/4 inches. Mix red sugar and cinnamon. Gently push fist into dough to deflate. Divide into 20 equal pieces; cover and refrigerate 8 pieces. Flatten each of the remaining 12 pieces into 2-inch round. Place 2 raisins in center for apple seeds. Bring sides of dough up over raisins; pinch edges to seal. Dip dough in melted butter to coat completely; coat with sugar-cinnamon mixture. Place pinched sides down in muffin cups. Insert handle end of wooden spoon about 3/4 inch in top of each, and rotate handle slightly to make indentation for stem. Cover loosely with plastic wrap and let rise in warm place 35 minutes.
4Heat oven to 375ºF. Bake 14 to 16 minutes or until rolls just begin to brown under coating. Immediately remove from pan to wire rack. Repeat steps with refrigerated pieces. Cool rolls 30 minutes. Break each cinnamon stick into fourths. Insert in indentations in apples for stems. Place mint leaf next to stem.