Preheat oven to 400ºF.

In a large bowl, mix together the warm water and 1½ teaspoons sugar. Sprinkle the yeast over the top, and let it stand for about 10 minutes, until the yeast is foamy. If your yeast and water mixture does not foam, your yeast may not be alive or the water was not at the correct temperature and you will have to repeat this step.

Mix the milk, eggs and salt into the yeast. Measure the flour into a separate bowl, add 1/3 cup sugar, and crumble the shortening into it using your fingers until it is barely noticeable. Gradually stir the flour into the wet ingredients. Mix using a wooden spoon until the dough pulls away from the sides of the bowl and starts to form a ball around the spoon. Remove the dough and knead on the counter (lightly floured) until it is a smooth consistency. 

Place the dough into a well buttered or greased bowl. I used metal mixing bowls as they helped with the warmth needed for the dough to rise. Cover lightly with plastic wrap that has been buttered or sprayed with oil to prevent it from sticking to the dough. Set in a warm place to rise until the dough doubles in size. This should take about 45 minutes to 1 hour.

When the dough has risen, return it to the floured counter and knead for about 2 minutes. Let the dough rest for a few minutes, then roll out to 1 inch thick. Use a knife or pastry scraper to cut into 2 inch squares. Roll squares into balls, and place into greased round pans or 11 X 9 baking pans, spacing about 1 inch apart. Let rise again covered with plastic you used before until doubled in size. You could also refrigerate the dough, and let it rise overnight for baking the next day.

Bake the rolls for about 12 minutes, until golden brown. Brush the top of the rolls with melted butter as soon as they come out of the oven; serve hot.

Note: It is essential that you have a kitchen thermometer for this recipe as you need the water at the correct temperature for the yeast to bloom and not too hot or it will kill the yeast. The warm water this recipe calls for should be 120 - 130˚F.