Dissolve yeast in ¼ cup of warm water. Combine yeast, sourdough, sugar, egg and butter/shortening. Add enough flour to make a soft dough (start with 2 cups and add more if dough is too sticky to be kneaded).
Turn out on a floured board and knead until smooth and satiny. Place in a greased bowl, cover with a towel, set in a warm place and let rise until doubled in bulk. Punch down and let rise a second time.
Grease a 13" x 9" pan.
Combine cranberries sugar and cinnamon and let sit for 10-15 minutes until sugar and juices turn into a syrup.
Roll out dough to a 12" x 18" rectangle. Spread cranberries across the rectangle.
Roll up jelly roll style along the shorter side. Cut into 12 rolls and place in the pan on top of the topping. Let rise again until rolls fill the pan.
Bake for 350°F for 45 minutes, until golden.
Combine powdered sugar, butter and vanilla together in a small bowl. Thin with milk until it reaches your desired consistency.