Combine the yeast mixture ingredients in a small bowl. Stir just until the yeast is dissolved. Cover with a towel and let stand until the mixture is foamy ~5 mins.
In stand mixer bowl, combine dough ingredients and yeast mixture, starting with 4 cups of flour, and mix. Slowly add more flour (~1 cup at a time) until the dough starts to pull away from the sides of the bowl.
Knead the dough with stand mixer for about 5 mins until the dough will just barely stick to your finger. Knead for 2-3 more mins.
Transfer the dough to a bowl coated with nonstick spray and flip dough so all sides are coated. Cover the bowl with a dish towel and let rise ~45 mins.
Divide the dough into 6 equal pieces Take each piece and pat down to remove any air. Gently fold into a tight ball. Place the dough balls on a baking sheet lined with parchment paper. Cover with a dish towel and let rise ~45 mins.
Make a small "X" slit on the top of each dough round and lightly brush the tops of each dough ball with egg wash mixture.
Bake at 400° F for about 25-30 mins. Allow to cool for at least 15 mins before cutting for bread bowls.