Press the tofu for 15 minutes to remove excess water, then slice into 1/2-inch thick rectangles to mimic halloumi slabs.
Use a fork to shred the king oyster mushroom stalks into long, thin strips to create a pulled donner-style texture.
In a medium bowl, toss the shredded mushrooms and tofu slabs with avocado oil, smoked paprika, cumin, garlic powder, salt, and pepper until evenly coated.
Heat a large non-stick skillet over medium-high heat and sear the tofu slabs for 3-4 minutes per side until they develop a golden, crispy exterior.
Add the shredded mushrooms to the same skillet and sauté for 5-7 minutes until they are browned and slightly caramelized.
In a small jar, whisk together the soy yogurt, lemon juice, and nutritional yeast until the sauce is smooth and creamy.
Warm the whole wheat pita in a dry pan or oven, then slice it open to create a pocket for the filling.
Stuff the pita with the mushroom donner and tofu slabs, then top with shredded red cabbage and sliced cucumber.
Finish by drizzling the tangy yogurt sauce over the filling and serve immediately while warm.