Preheat the oven to 375°F (190°C). Lightly grease a 9×13-inch baking dish.
Place the butterflied flank steak on a cutting board and gently pound it with a meat mallet until evenly thin.
Heat the vegetable oil in a skillet over medium heat.
Add the mushrooms, onion, garlic, and parsley. Cook for 7–9 minutes until most of the moisture has evaporated. Let cool slightly.
Season the steak with 1 teaspoon salt and 1/2 teaspoon white pepper.
Spread the mushroom mixture evenly over the steak, leaving about 1/2 inch around the edges.
Sprinkle the feta cheese evenly across the filling.
Carefully roll the steak tightly from one end and secure with kitchen twine every 1–2 inches.
Rub the outside with olive oil.
Combine the remaining salt, white pepper, smoked paprika, garlic powder, and onion powder, then coat the outside of the roast evenly.
Place the rolled Stuffed Flank Steak into the prepared baking dish.
Pour the beef consommé around the roast rather than over the top.
Bake for 35–40 minutes or until the internal temperature reaches:
125°F for rare
130–135°F for medium-rare
140°F for medium
Remove from the oven and let rest for 10 minutes.
Slice into thick pinwheels and serve immediately.