
Rotate the meat about 45 degrees, keeping it on the same side, and cook for another 1 ½ minutes. Cook without touching for about 1 ½ to 2 minutes. When the pan is extremely hot, place the steak on a slight angle as this makes for more appealing grill marks. Make sure to turn on your overhead exhaust fan as the cooking process can be quite smoky. Remove the steak from the marinade and place on a plate while you heat up the grill pan.
Coat both sides of the meat with marinade. Remove flank steak from package and give it a quick rinse.
Combine all ingredients in a glass or ceramic dish. Drizzle the sauce over the steak, drizzle a little more extra-virgin olive oil and serve. Thinly slice the steaks across the grain. Season the sauce, to taste, with salt and pepper. Cut the remaining 4 tablespoons of butter into small 1/2-inch chunks and whisk in the sauce a little at a time. Discard the solids in the strainer and return the sauce to the saucepan and bring back to a slow simmer. Strain the sauce into a small bowl, pressing on the solids to extract as much liquid as possible. Simmer until the sauce reduces by half, stirring occasionally, about 10 minutes. Stir in the tomato paste and cook for 2 minutes, stirring constantly. Add the garlic and oregano and saute until fragrant, about 30 seconds. Add the onions and saute until tender, about 5 minutes. Meanwhile, melt 2 tablespoons of butter in a heavy large saucepan over medium-high heat.
Grill to desired doneness, about 5 minutes per side for medium-rare. Sprinkle the steaks with salt and pepper and drizzle with the 3 tablespoons of olive oil. Prepare the grill or barbecue (medium-high heat).