Cut horizontally through center of steak, cutting to, but not through, the other side and open flat, like a book; place between 2 sheets of heavy-duty plastic wrap and flatten to an even thickness using a meat mallet or rolling pin.
Spread spinach mixture over steak, leaving a 1-inch margin around outside edges and roll up, jelly-roll fashion, starting with short side; secure with heavy string at 2-inch intervals.
Coat a large Dutch oven with cooking spray and heat at medium-high until hot (I drizzle the pan with olive oil, rather than using cooking spray).
Add steak, browning well on all sides; add broth, wine, water, and oregano and bring to a boil.
Cover, reduce heat and simmer 1 hour and 30 minutes, or until tender, turning meat once; add additional water during cooking if necessary.
Remove string and cut steak into 8 slices; serve with cooking liquid.