Heat the olive oil in a medium sized pan over medium-high heat. Add the onion and cook for about 5 minutes, until it becomes translucent and fragrant.
Add the garlic and cook for another minute or two.
Add the seitan, oregano, thyme, cumin, salt, and pepper to the pan and cook for about 10 more minutes, stirring frequently, until the seitan browns and the edges begin to crisp. Remove from heat.
Place the flat breads or pitas on a plate and top (or stuff) with the lettuce, carrots, tomatoes, and cucumber. Divide the seitan equally among each sandwich and top with the tahini and parsley.