Dissolve yeast in milk in a large bowl. Stir in egg, sugar, and salt. Add whole wheat flour and shortening, mixing well. Gradually add all-purpose flour to form a stiff dough, beating well after each addition.
Place dough in a lightly greased bowl, turning to grease top. Cover and let rise in a warm place (85°), free from drafts, for 1 1/2 hours or until doubled in bulk. Punch down; cover and let rise 30 minutes or until doubled in bulk.
Lightly grease muffin pans. Shape dough into 2-inch balls; place 1 ball in each muffin cup. Brush tops with melted butter. Cover, and let rise 45 minutes or until doubled in bulk. Bake at 400° for 12 to 15 minutes or until golden brown.