In a medium sized baking bowl, whisk together flour, yeast and water for 2 min until dough is thick and smooth. Scrape the sides of the baking bowl clean, cover the baking bowl with plastic wrap and let stand at room temperature for 1-4 hours. For best flavor development, let dough stand at room temperature for 1 hour, then refrigerate for 8-24 hours. Remove from refrigerator 1/2 hour before further processing and shape in the wide bowl of a food processor.
Grate the parmesan and pecorino. In a measuring cup with a spout, stir through the water and egg.
In a medium baking bowl, stir through the flour (all but a scant quarter cup), yeast, salt and black pepper. Pour this mixture over the dampfl form.
Add the softened butter and mix it all together with the dough hook at low speed, while slowly adding the water-egg mixture. Then add the grated cheese, increase the speed to medium and knead for 5 min until the dough is elastic and still slightly sticky. If the dough still does not separate from the walls of the baking bowl, gradually knead in the remaining flour.
Shape the dough onto the lightly floured surface and press into a rectangle. Press 1/2 cup of the Gruyère into the dough, roll it up, and knead to distribute the cheese evenly. (The dough should now weigh 1050-1060 grams).
Now place the dough in a lightly oiled baking bowl of about 2 liters F