Preheat the oven to 220℃.
Line a baking tray with some parchment paper.
Dust the work top with little flour.
Unfold the pastry and gently roll it out to about 10 inches wide and 13 inches long.
With the length side towards you brush the olive oil all over the puff pastry.
On one half of the side sprinkle all the za'atar.
Cover the za'atar part with the other half part that is plain.
Turn the pastry 90°. The longer side will be towards you.
Using a pizza or pastry cutter cut into strips about an inch apart.
use a ruler for guidance. You should get 10 strips.
Take one strip. holding both ends, twist it gently.
Lay it on the work surface. Roll it into a swirl or spiral.
Repeat the same with the other strips.
Put the tray with the za'atar swirls in the fridge for 20-30 minutes.
Take the tray out of the fridge.
Brush the top of each swirl with some milk or whisked egg.
Sprinkle sesame seeds over them.
Bake the za'atar swirls for 20-25 minutes or till they are golden brown.
Take the za'atar swirls out of the oven.
Put the swirls on a wire rack to cool for a few minutes.
Serve warm za'atar swirls.
As the za'atar is full of flavours you wouldn't need a dip to go with the swirls. If you want to serve them with a dip opt for whipped feta dip.