Make the shawarma spice blend. In a small bowl, combine 2 tsp ground coriander, 1 tsp turmeric, 1 tsp sumac, 1 tsp garlic powder, 1 tsp cumin, 1 tsp Kosher salt, ½ tsp sweet paprika, ½ tsp ground cardamom, ¼ tsp ground cinnamon, and a pinch of Cayenne pepper (or more if you want it spicier). Mix well.
Season the mushrooms. Drizzle the mushrooms with 2 Tbsp olive oil, then sprinkle the shawarma spice blend on top. Toss to thoroughly coat.
Sear the mushrooms. Heat a large cast-iron skillet over medium-high heat. When hot, add 2 Tbsp olive oil, let it heat up, then add the mushrooms. Weight them down with a food weight or another large heavy pan. Cook undisturbed for 5 minutes, then flip them over or give them a good stir. Repeat and cook for another 3-5 minutes, or until they’re nice and crispy.
Make the white sauce. While the mushrooms are cooking, combine ½ cup mayo, ¼ cup sour cream, 2 Tbsp white vinegar, 1-2 cloves of grated garlic (use 2 if you like it extra garlicky!), 1 tsp sugar, ½ tsp Kosher salt, and ¼ tsp black pepper. Whisk until smooth, then add a few teaspoons of water, as needed, to reach desired consistency for drizzling.
Assemble, then serve! Pile onto warm pita bread with tzatziki (or white sauce), chopped lettuce, cucumbers, tomatoes, and pickled red onions. Drizzle with tahini, then serve with lemon wedges.