To make the vinaigrette, place all ingredients in a jar with a tight-fitting lid. Shake, shake, shake. Set aside. Shake again vigorously before using.
Place potatoes in a medium saucepan and cover with cold salted (1 teaspoon salt) water by 2 inches. Cover and bring to a boil, reduce heat and simmer until tender, 8 to 12 minutes. Drain and cut in half. Toss with 3 tablespoons vinaigrette in a bowl. Let sit, stirring occasionally, while the steak is cooking. Most of the dressing will be absorbed.
Meanwhile, grill the steak.
To cook on a gas or charcoal grill, prepare grill (high heat). Season steaks with 1 teaspoon salt and ½ teaspoon freshly ground black pepper. Place steaks on the grill rack and cook to desired doneness, about 5 minutes per side 135˚F for medium-rare, 140˚F for medium. Remove steaks from grill; tent loosely with foil and let stand 10 minutes. Thinly slice steaks across the grain.
For pan grilling, heat 2 teaspoons sunflower oil (or other neutral flavored oil) in a heavy bottomed skillet over medium-high heat. Season steak with 1 teaspoon salt and ½ teaspoon pepper. Cook, partially covered, until the internal temperature registers 135°F for medium-rare, 140˚F for medium, about 5 to 7 minutes per side, or to the desired degree of doneness. Remove steaks from pan; tent loosely with foil and let stand 10 minutes. Thinly slice steaks across the grain.
To serve, arrange arugula (or other greens) on a large serving platter or on individual serving plates. Top with warm steak, potatoes (warm slightly in the microwave, if desired) and cherry tomatoes. Scatter with Feta cheese and scallions. Drizzle with 2-3 tablespoons of dressing, then sprinkle salad with fresh dill, a bit of sea salt and more freshly ground black pepper. Serve extra dressing at the table.