In a large saucepan, over medium-low heat, combine milk, buttermilk, honey, brown sugar, and shortening.
Stir until shortening has melted, do not boil.
Remove from heat and allow mixture to cool to 115 degrees F.
Meanwhile, whisk together 1 ¼ cups flour and yeast in a large bowl. Set aside.
Once the liquid mixture reaches the appropriate temperature, add it into the flour-yeast mixture, stirring to incorporate.
Mix in the egg and salt.
Gradually add the remaining flour, using a rubber spatula to incorporate.
Turn the dough onto a lightly floured surface and knead just until the dough is smooth (may need to add a tad bit more flour to keep the dough from sticking to your hands but be sure not to add too much. After kneading the dough should be soft and smooth, not dry and crumbly)
Place dough into a large greased bowl, and turn the dough so that it is coated in oil.
Cover bowl with plastic wrap and place into the oven with the pilot light on or in a very warm location to rise.
Let dough sit until it is doubled in size (about 1 ½ to 2 hours)
Remove plastic wrap and punch dough to remove air.
To create the rolls, remove about 2 tablespoons of dough and flatten on the palm of your hand.
Brush with melted butter and fold both sides onto each other.
Place seam side down into a greased 9 x13 casserole dish.
Repeat until all rolls have been created.
Brush the tops with butter.
Cover with plastic wrap and return to oven with pilot light on or to a warm location.
Let rolls sit for about 60 minutes or until they have filled out in the pan.
Remove from oven and preheat the oven to 400 F.
Remove plastic wrap and bake rolls for 12-14 minutes. *
When done, brush the hot rolls with remaining butter.