Drizzle the steak with extra-virgin olive oil. Season with salt and pepper.
Cook, turning once, for medium rare 8-10 minutes.
Let cool slightly then slice thinly.
While steak is cooking or cooling, use a food processor to puree the feta, yogurt, lemon juice, garlic, oregano, cumin, coriander, and hot sauce. Season with salt and pepper and transfer to a bowl. Leave in fridge to cool if you'd like.
Char the pitas under the broiler or grill. Top with steak and your choice of toppings (see optional items above). Serve with lemon wedges and yogurt sauce.