In a small jar or bowl with a lid, combine 2 tablespoons olive oil, 2 tablespoons lemon juice, minced garlic, cumin, and sumac. Close and shake or whisk until well combined; this is your marinade and dressing.
Reserve half of the dressing for the salad. Spoon the other half over both sides of the flank steak, then season both sides generously with kosher salt and freshly ground black pepper.
Let the steak sit at room temperature for 30 minutes (or refrigerate and marinate overnight if preferred).
Preheat the broiler to high and position a rack so the steak will be a few inches from the heat. Place the steak on a rimmed baking sheet and broil for about 5 minutes on the first side, then flip and broil 4 to 5 minutes more, adjusting time for desired doneness.
Transfer the steak to a cutting board and let it rest for 10 minutes before slicing.
While the steak rests, in a bowl toss the arugula, sliced scallions, and parsley with the reserved dressing. Season the salad with salt and pepper to taste.
Slice the steak thinly against the grain. Arrange the slices on a platter, top with the dressed arugula mixture, and scatter crumbled feta over the top.