In a bowl, whisk together all the ingredients for the shawarma marinade until well combined.
Add the sliced mushrooms to the marinade and toss until they are evenly coated. Let them marinate for at least 30 minutes, or longer if possible, to allow the flavors to develop.
While the mushrooms are marinating, prepare the vegan tzatziki. In a separate bowl, combine the vegan yogurt, grated cucumber, minced garlic, lemon juice, chopped dill, salt, and pepper. Mix well and refrigerate until ready to use.
Heat a large skillet over medium-high heat. Add the marinated mushrooms to the skillet and cook for about 8-10 minutes, or until they are tender and slightly browned, stirring occasionally.
Warm the flatbread according to the package instructions or lightly toast it if desired.
To assemble, spread a generous amount of vegan tzatziki on the flatbread. Top with the cooked mushrooms, sliced tomatoes, and onions.
Fold the flatbread over the filling to create a wrap or roll it up tightly.
Serve the vegan mushroom shawarma immediately and enjoy!
Note: Feel free to add additional toppings or garnishes such as fresh herbs, pickles, or hot sauce to customize your mushroom shawarma to your liking.