Preheat oven to 400˚F (200˚C). Place a pizza stone or large round baking sheet on the center rack of the oven.
On a lightly floured surface, roll the risen dough into a large, thin circle. Place the filling in the center, spreading it out into a flat layer, leaving a large border around the edges.
Fold the edges in towards the center and seal the edges well to completely cover the filling. Flip the bread over, seam-side down, and gently pat or roll to create a smooth, stretched circle with the filling sealed inside.
Pierce the top of the bread all over with a fork and brush with the beaten egg.
Transfer to the stone or hot pan in the preheated oven and bake until golden, 30-40 minutes. The bread may puff, but will settle back down when removed from the oven.
Immediately brush the top with butter. Cut into wedges and serve hot.