Use a meat mallet to tenderize and flatten the 2 pound flank steak. The thinner the steak, the easier it will be to roll, but you also want to avoid making holes. Instructions on how to butterfly your roast are in the note section. You can also ask the butcher to do this for you.
Preheat the oven to 375°F. Coat the bottom of a 9x13 inch glass baking dish with cooking spray. Set aside.
Heat the 1 teaspoon vegetable oil in a medium skillet over medium heat. Add the chopped 1 cup mushrooms, chopped 1/4 cup sweet onion, minced 3 cloves garlic and chopped 2 tablespoons Italian parsley, cooking until reduced in volume by at least half, approximately 7-9 minutes. Remove the skillet from the heat and allow to cool slightly.
Lay the butterflied flank steak out on a cutting board. Season it with 1 teaspoon of the salt and 1/2 teaspoon of the white pepper. Evenly distribute the mushroom mixture, leaving about 1/2 inch along the edges. Evenly distribute the crumbled 1/2 cup feta cheese
Roll the steak along the grain into a roll. Fasten with the cooking twine. The twine should be tight enough to hold it in a roll, but not so tight that your filling is being pushed out.
Rub the exterior of the roast with the 1 tablespoon extra virgin olive oil on the exterior of your rolled flank steak. In a small bowl, mix together the remaining 1 teaspoon of salt, 1/2 teaspoon of white pepper, s1 teaspoon smoked paprika , 1/2 teaspoon garlic powder and 1/2 teaspoon onion powder. Rub this into the tied roast and transfer it to the prepared baking dish.
Pour the 10 ounces beef consume into the bottom of the baking dish (not over top of the roast).
Bake for 35-40 minutes, or until the roast is between 125°F (rare)-140°F (medium) using a digital internal thermometer.
Remove the roast and allow it to rest for 10 minutes before slicing into pinwheels.
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Notes
If you weren't able to find a butterflied flank steak at the store (or the butcher wasn't able to do it for you,) you might need to prepare your flank steak. You are aim for 1/4- 1/2 inch thickness. Lining a very sharp knife parallel with your cutting board and slice through the center of the steak, stopping just short of cutting all the way through. You should be able to open it up like a book and the surface area of the meat will have doubled.