Preheat oven to 200C/400F.
Line a baking tray with baking paper.
In a large bowl, mix all the ingredients for the marinade. Dip the mushrooms in the marinade and turn each piece to coat them evenly.
Spread the mushrooms on the baking tray, in a single layer and bake them in the oven for about 20 minutes.
Take the mushrooms out of the oven, slice and put them back to broil, for 4 or 5 minutes more. Let them cool a bit.
While the mushrooms are baking, prepare the sauce by mixing all the sauce ingredients in a small dish.
To assemble the wraps, spread 2 tablespoons of hummus on each wrap and sprinkle with zaatar Divide the mushroom slices between the wraps. Top with tomatoes, cucumbers, lettuce, white sauce, and parsley. Roll up and enjoy.