Start with the sweet roll dough. For regular yeast, dissolve yeast in warm water. Stir in milk, sugar, salt, eggs, shortening, and half of the flour. Beat until smooth. Add enough flour to make dough easy to handle. (For rapid rise yeast, mix yeast with half of the flour. Heat water, milk, and shortening. Add to flour. Add sugar, salt, and eggs. Beat until smooth.)
Turn dough onto a lightly floured board; knead until smooth and elastic, about 5 minutes. Place in a greased bowl and turn greased side up. At this point, if you used regular yeast, the dough can be refrigerated for 1-2 days. Cover and let rise in warm place until double the size – about 90 minutes. Dough is ready if impression remains when touched. (For rapid rise yeast, let the dough set for 15-30 minutes. Roll and shape into rolls. Then let rise 60 minutes or so until rolls are puffy.)
To make the filling, beat powdered sugar, butter, orange peel, and orange juice until creamy.
Roll dough into a rectangle, 12x7 inches, on a lightly floured surface; spread with half of the orange mixture. Roll up tightly, beginning at the 12-inch side. Pinch edge firmly to seal. Stretch roll to make even. Cut into 12 1-inch slices. Place slightly apart in greased round baking pan, 8x1 1/2 inches. Let rise until double the size, about 40 minutes.
Heat oven to 375˚. Bake until golden brown, 20-25 minutes. Frost with remaining orange mixture while warm.