Stir together 1/4 cup warm water, yeast, and 1/4 cup sugar; let stand 5 minutes.
Combine yeast mixture, 1 3/4 cups flour, milk, salt, egg, and shortening in a large mixing bowl. Beat at medium speed with an electric mixer until well blended. Gradually stir in enough remaining flour to make a soft dough.
Turn dough out onto a well-floured surface; knead until smooth and elastic (about 5 minutes). Place in a well-greased bowl, turning to grease top.
Cover and let rise in a warm place (85°), free from drafts, 1 1/2 hours or until doubled in bulk.
Punch dough down, and cover and let rise in a warm place, free from drafts, 30 minutes or until dough is doubled in bulk.
Turn dough out onto a floured surface, and roll dough to a 15- x 9-inch rectangle. Spread with butter, and sprinkle with remaining 1/2 cup sugar and cinnamon.
Roll up, jellyroll fashion, starting at a long edge. Cut dough into 1-inch slices. Arrange in a lightly greased 13- x 9-inch pan.
Cover and let rise in a warm place, free from drafts, 30 to 40 minutes or until doubled in bulk.
Bake at 375° for 17 minutes or until done. Stir together powdered sugar, 3 to 4 tablespoons milk, and vanilla until blended, and drizzle over rolls.