Heat oven to 200C/180C fan/gas 6 and line a baking sheet with baking parchment. Unroll the croissant dough and use a knife to separate the dough triangles. Scatter all of the cheddar, ¾ of the parmesan and 1½ tbsp of the za’atar over the dough triangles, pressing the mixture in with your hands so that it sticks.
Starting from the base of one triangle, roll the dough upwards towards the narrow point. Bend each end in slightly to form a croissant shape. Repeat with the remaining dough. Put the croissants on the lined baking tray, brush each one with the beaten egg and sprinkle over the remaining parmesan and za’atar. Bake for 15-20 mins until deep golden brown.