Preheat oven to 400F degrees. Line a large baking sheet with parchment paper.
Shape the pizza dough into a large rectangle. Roll all four edges inwards about 1-2 inches. Pinch the top and bottom ends together so that the dough resembles a boat.
Transfer the dough to the prepared baking sheet.
In a small bowl, combine both cheeses and 1 egg. Using the back of a spoon, spread the cheese mixture inside the dough boat.
Bake for 8 minutes. Remove from the oven, brush the outer crust with the melted butter and sprinkle with sesame seeds. Crack the remaining egg over the cheese mixture, being careful not to break the yolk. (Alternatively, strain out the egg whites and just place the egg yolk onto the cheese.)
Bake an additional 8 minutes, until crust is golden brown and egg is set. Serve warm.