Preheat the oven to 400°F. Using a sharp knife, cut the super-firm tofu into very thin slices. A mandoline also works well. If using extra-firm tofu, press it for at least 15 minutes first to remove excess liquid.
Thinly slice the onion. Thinner slices will become caramelized and slightly crisp as they bake, while thicker slices will stay softer.
In a large bowl, whisk together the olive oil, soy sauce, lemon juice, and all the spices.
Add the tofu and thinly sliced onion and gently toss until evenly coated. Don't worry if some of the tofu breaks apart. This is a good thing! The smaller pieces become crisp while the larger pieces stay chewy. For easier coating, use a bowl with a lid and gently shake rather than tossing with a spatula.
Spread the tofu and onions evenly on a large baking sheet. Try to avoid too much overlap so everything can brown evenly.
Bake for 25-30 minutes, tossing a few times throughout to prevent the onions from burning. The tofu is done when it's browned and slightly crisp around the edges.
While the tofu is baking, add the vegan yogurt, tahini, lemon juice, garlic, olive oil, salt, and black pepper to a small bowl. Stir until smooth and creamy. Finely chop the dill and parsley, then stir them into the sauce. Taste and adjust as needed.
Serve warm on flatbread with lettuce, cucumber, tomato, pickled onions, and plenty of yogurt sauce. Enjoy!