Place the flour and salt in the bowl of an electric mixer fit with the paddle attachment. While mixing on medium speed, add the water, then the egg, and mixing for 1 minute.
Shape the dough into a ball, cover with plastic wrap, and let rest 30 minutes.
Place a baking dish full of water in an oven set to 230°C (450°F).
On a floured surface, roll the dough to a rectangle. Cut it lengthwise into two long strips.
Spread the butter on the dough. Roll the first strip into a cylinder, then place it on the second strip and roll the whole into a thicker cylinder. Cover with plastic wrap, and refrigerate for at least 1 hour.
Place the unwrapped cylinder of dough vertically on a floured surface. Using the palm of your hand, flatten the dough progressively to a 1½ cm (½") thick, 18 cm (7") diameter disc. While doing this, sprinkle the top generously with flour, and flip the dough frequently — otherwise your dough will be stuck to the counter in a puddle of grease!
Prick the flatbread with a fork to create a decorative pattern, then sprinkle the sesame seeds on top and gently press with the palm of your hand to encrust the seeds in the dough.
Transfer to a baking sheet lined with parchment paper, and bake in the oven for 25-30 minutes, until the top is golden brown. Transfer to a cooling rack, and reserve.