Grate the Parmesan and Romano or Pecorino cheeses with a hand grater. Set aside.
In a measuring cup with a spout, whisk together the water and egg.
In a medium bowl, whisk all but a scant 1/2 cup of the flour, the yeast, salt, and black pepper. Sprinkle the mixture over the sponge.
Add the softened butter and mix with the dough hook on low speed while gradually adding the water/egg mixture until the flour is moistened, about 1 minute. Add the Parmesan and Romano/or Pecorino cheese, raise the speed to medium and knead the dough for 5 minutes or until elastic and bouncy. The dough should be slightly sticky. If it does not pull away from the bowl, beat in some or all of the remaining flour by the tablespoon. The dough should feel slightly sticky.
Empty the dough onto a lightly floured counter and flatten it into a rectangle. Press 1/2 cup of the Gruyére into the dough, roll it up, and knead it to incorporate evenly.
Place the dough in a 2-quart dough-rising container or bowl, lightly greased with cooking spray or oil. Push down the dough and lightly spray oil the top. Cover the container with a lid or plastic wrap -- I use a shower cap. With a piece of tape, mark the side of the container at approximately where double the height of the dough would be. refrigerate the dough. Allow it to chill for at least 8 hours or up to 2 days to firm and ripen (develop flavor). Pat it down two or three times after the first hour or two , until it stops rising. Once the dough is cold, it will stop rising.
Following day turn the dough out onto a counter and knead it lightly. Round it into a ball and push it down into the oil sprayed soufflé dish. Spray the dough top and cover it lightly with a piece of wax paper and let it rise in a warm area ( 80 to 85 F) until it almost triples, about 3 to 4 hours. The center should be at least 1/2 inch, preferably 1 inch, above the top of the dish.
Preheat the oven to 350 F 45 minutes before baking. Have an oven shelf at the lowest level and place a baking stone or baking sheet lined with foil on it before preheating.
Glaze, stud, and bake the bread. Brush the surface of the dough with the lightly beaten egg, being careful not to brush it on the insides of the dish , which would impede rising. Gently insert the remaining 2 Tablespoons Gruyère cubes into the dough using a chopstick; first gently twist it into the dough to make a shallow hole, then use the chopstick to push in a cheese cube; it should be visible. Don't by shy with the cheese -- I do use more than the 2 Tablespoons -- we really like cheese.
Place the dish on the hot stone or hot baking sheet. Bake for 45 to 50 minutes or until the bread is golden and a skewer inserted in the middle comes out clean (an instant-read thermometer inserted into the center will read about 190 F.
Remove the pan from the oven and set it on a wire rack for 30 minutes. With the tip of a sharp knife, loosen the sides of the bread where the cheese may have crusted and unmold the bread onto its side onto a soft pillow (covered with a piece of plastic wrap and then a clean dish towel towel) on the counter to finish cooling. This will prevent the soft fragile sides from collapsing; turn the loaf a few times to speed cooling, but always leave it on its side. It will take about 1 hour to cool completely.
The bread stays moist and soft for 2 days but is really good lightly toasted or heated for 3 to 4 minutes in a 400 F oven to remelt the cheese.