In a small bowl, dissolve yeast in the warm water. Set aside.
In small saucepan, bring milk to a simmer, then remove from heat immediately. While milk is coming up to a simmer, measure shortening and sugar into a large bowl. Pour hot milk over shortening and sugar.
Whisk to melt and dissolve all ingredients together.
Stir in whole wheat flour and cool to lukewarm {105 to 115 degrees F}.
Transfer mixture to a stand mixer. Add in one egg, salt and 2 cups of flour. Stir in yeast mixture. Using the dough hook, knead in all purpose flour bit by bit until dough is moderately stiff and almost completely smooth. *You may not use all the flour listed, and that's ok!* Dough will be done when tacky but not tacky enough to stick to your hands when touched.
Grease a large bowl and place dough in, turning once to grease surface of dough. Cover with a clean dish towel and rise 1-1 1/2 hours or until doubled in size.
Spray two 9x13 glass pans with nonstick cooking spray and set aside. Punch dough down. Remove from bowl onto clean work surface.
Cut in half evenly and then cut each half into 12 even pieces. Roll each piece into a ball and place into prepared pans. Cover and let rise until rolls are puffed and touching each other; 30-45 more minutes.
Brush the tops of each roll with beaten egg.
Bake at 350 for 20-25 minutes or until lightly browned. Cool 5 minutes before serving warm with lots of butter.