Start by butterflying the flank steak. Place the steak on a cutting board, and with your sharp knife, carefully slice it horizontally, stopping just before you cut all the way through. Open the steak like a book and pound it gently with a meat mallet to an even thickness of about ½ inch.
Generously season both sides of the butterflied flank steak with salt and freshly ground pepper. This step is crucial for enhancing the flavor of the meat.
In a skillet, heat the olive oil over medium heat. Add the chopped mushrooms and minced shallot, sautéing until the mushrooms are tender and the shallots are translucent, about 5 minutes. Stir in the fresh thyme and cook for an additional minute. Remove from heat and let it cool slightly.
Spread the sautéed mushroom mixture evenly over the seasoned flank steak, leaving a small border around the edges. Layer the sliced Provolone cheese and packed baby spinach on top of the mushroom mixture.
Starting from one end, carefully roll the flank steak tightly into a log shape. Secure the roulade with kitchen twine at both ends and in the center to keep the filling intact during cooking.
Preheat your oven to 375°F (190°C). Place the roulades seam-side down in a baking dish. Bake for 25-30 minutes, or until the internal temperature reaches 145°F (63°C) for medium-rare. If you prefer your steak cooked more, leave it in the oven for an additional 5-10 minutes.
Once baked, remove the roulades from the oven and let them rest for 10 minutes before slicing. This resting period allows the juices to redistribute, ensuring a tender and juicy bite. Slice into 1-inch thick pieces and serve warm.