In a large bowl, combine all the marinade ingredients and mix well. Add the chicken slices and let them marinate for at least 1 hour.

In a skillet over medium heat, melt a pat of butter. Add the marinated chicken mixture and cook, stirring, until almost done. Add the vegetables, all thinly sliced, and continue cooking until everything is fully cooked. Fill each flatbread with the shawarma mixture and roll them up tightly. Grease a baking dish with a little butter and arrange the rolls inside.

Brush the rolls with some of the leftover shawarma marinade and bake until golden. Remove from the oven, sprinkle with the cheeses and a little dried thyme, then return to the oven until the cheese melts.

Take them out and serve hot. Enjoy!