Butterfly the flank steak, or slice it horizontally almost all the way through so it opens like a book. Pound to an even thickness and season both sides generously with salt and pepper.

Heat olive oil in a sauté pan over medium heat. Add mushrooms, shallot, and thyme, cooking until soft. Then add spinach and cook just until wilted. Let mixture cool before assembling.

Preheat oven to 350°F. Lay the beef flat with the grain running left to right. Cover with Provolone, leaving a 1-inch border, and spread the spinach mixture on top.

Roll the steak up tightly away from you and tie with butcher's twine at 2-inch intervals.

Place in a greased baking dish or on a rack in a roasting pan. Roast for 45 minutes to 1 hour, until the internal temperature reaches about 130°F for medium-rare.

Cover with foil and let rest for 10 minutes before slicing.