Dissolve yeast in 1/2 cup milk. Stir in remaining milk, the sugar, salt, eggs, shortening and 5 cups flour. Beat until smooth, adding more flour as needed to make the dough easy to handle.
Turn dough onto lightly floured board and knead until smooth and elastic, about 5 minutes. Place in greased bowl and turn greased side up. Cover and let rise in warm place until doubled.
Shape into rolls. Dip in melted butter. Place in greased muffin cups or 3 inches apart on greased baking sheets. Let rise again, then bake at 325 degrees F for 20-30 minutes. Brush again with melted butter.