Combine all the stuffing ingredients in a food processor and process until they form a smooth paste, about 45 to 60 seconds.
Prepare the flank steak by placing it between plastic wrap and pounding to a thickness of 1/3 inch; score on one side in a criss-cross pattern. Turn the steak over and season well with salt and pepper. Smooth all but 1 tablespoon of the stuffing over the entire steak; reserved stuffing will be used later in a sauce. Roll steak up and tie with kitchen twine in about 3 places. Place the steak, uncovered, in the refrigerator for at least two hours up to overnight (you want the outside to dry a bit and the inside to marinate).
Preheat oven to 375 degrees F and bring the steak to room temperature. Heat a large skillet over medium high heat; season steak on all sides generously with salt and pepper and sear well, in a little oil, on all sides.
Meanwhile combine reserved stuffing mixture, water, mustard, garlic, rosemary, and oils in a roasting pan or baking dish; place a rack for the meat on top. Place the meat on the rack, brush with pan juices, and roast to an internal temperature of 120 degrees F, about 15 minutes.
Let rest about 15 minutes, then slice into 1/4 inch slices; drizzle with pan sauce and more extra virgin olive oil if desired.