Dissolve yeast in warm water (110-115F degrees) until bubbling, about 10 minutes.
In the bowl of a stand mixer fitted with the paddle attachment, beat 3 eggs, butter, sugar and salt on medium speed.
Pour milk into a small saucepan. Warm the milk to 115 degrees. Pour the warm milk into the stand mixer. Then, pour in the yeast mixture.
Preheat the oven to 200 degrees.
Change out the paddle attachment for the dough hook attachment. Turn the mixer on to low speed and add 5 1/2 cups of flour, one cup at a time, until the dough pulls away from the sides of the bowl and a ball forms.
Use the remaining 1/2 cup of flour to dust a work surface. Knead the dough ball on the work surface for 7-8 minutes, until smooth.
Transfer the dough to a buttered bowl. Cover with a dish towel. Turn off the oven and place the bowl into the warm oven for 90 minutes.
Remove the dough from the oven and punch it down. Portion the dough into 16 balls. Place the balls into a round 15" buttered pan. (Alternatively, use 2 round 8" pans or pie plates.) Cover with a dish towel and rest for 1 hour.
Preheat oven to 375 degrees.
In a small bowl, beat the remaining egg with 2 tsp. of water. Brush the dough with the egg wash. Cover the baking dish with aluminum foil. Bake 15 minutes. Remove the foil and bake another 15 minutes. Allow the rolls to cool completely before removing from pan.