Place 2 cups flour in a large mixing bowl. Add yeast, salt, sugar and dry milk. Set aside.
In a mixing bowl, combine water and egg and stir to blend.
Make a well in the center of the dry ingredients. Pour water mixture into the well.
Mix by hand, beating 150 strokes and frequently scraping bottom and sides of bowl.
Add 1/2 of the melted butter and beat to incorporate. Add remaining flour, about 1/3 cup at a time, beating to incorporate each addition.
Cover bowl with plastic wrap. Set dough in a warm, draft free place such as oven with a pan of the hottest tap water on the rack below.
Allow batter to rise until doubled in bulk, about 1 hour.
Coat cups, bottoms and sides of 12 cup muffin pan (or two small round pans) with shortening. Punch down batter (batter will be extremely soft and sticky). Drop by hand or spoonful into prepared muffin cups to make 12 rolls (or in pan touching the next). Brush dough with 1/2 remaining melted butter.
Let rise uncovered in a warm draft free place until doubled in bulk, about 30 minutes. In preheated 400 degree oven, bake rolls on middle rack for 16-18 minutes.