Add all of the dough ingredients to a large bowl or a stand mixer fitted with a dough hook. Mix to incorporate and then knead until you have a soft, smooth dough.
Lightly grease a large bowl and place the dough in it. Cover the bowl with plastic wrap or a damp tea towel and let rise in a warm place for about an hour, or until the dough is almost doubled in size.
When the dough is ready, divide it into four equal pieces.
Roll each piece of dough out into a 10" round.
Place the first circle of dough onto a parchment-lined baking sheet. Brush the surface lightly with the beaten egg, leaving 1" space without egg around the edge.
In a medium bowl, mix the dried herbs, salt, and garlic powder with the softened butter to form a well-mixed paste.
Spread 1/3 of the herbed butter in a thin layer over the egg. Sprinkle 1/3 of the grated cheese over the filling.
Place the second circle of dough on top of the filling. Repeat with the butter and cheese, top with the next circle of dough, repeat with the filling, then top with the final circle of dough.
Trim the edges of the circles if they aren't even. Place a 2" wide drinking glass, biscuit cutter, or other circular object in the center of the top circle of dough.
Using a very sharp knife, cut through the dough from the outer edge to the edge of the circular object in the center. Cut sixteen equal slices.
Take two slices of dough and twist them away from each other twice. Repeat around the entire circle. Take each pair of twisted slices and press the ends together firmly to seal the dough.
Cover loosely with plastic wrap and let the dough rise for 15 minutes, while you preheat the oven to 400 degrees F.
Brush the top of the loaf with beaten egg and bake it for 15 minutes, or until lightly golden brown.
Remove from the oven and let cool slightly before serving.