Combine zaatar, oregano, cumin and a generous pinch of salt and pepper in a small bowl. Drizzle in 1/4 cup olive oil until a thick paste forms. Rub the steaks with the spice mixture and let sit at room temperature for 45 minutes.
Meanwhile, place the potatoes in a large pot and cover with cold water by 2 inches. Season water generously with salt and bring to a low boil over medium heat. Let cook until the potatoes are slightly tender but not cooked through entirely, 20 to 25 minutes. Drain, and once cool enough to handle, thread 4 or 5 potatoes on each of 5 metal skewers.
Whisk together white wine vinegar, miso and 2 tablespoons olive oil in a large bowl. Add parsley, dill and capers. Add tomatoes, cucumber and olives and season with salt and pepper. Toss to coat and set aside.
Preheat the grill or a grill pan to medium-high heat. Grill the steaks to desired doneness, 4 to 5 minutes per side for medium. Let rest for 5 to 10 minutes before slicing.
Meanwhile, drizzle remaining 2 tablespoons olive oil over potatoes and sprinkle generously with salt and pepper. Grill until skin is crispy and potatoes are cooked through, 4 to 5 minutes per side.
Slice steaks 1 1/2-inch thick and top with salad. Sprinkle with feta and serve with grilled potatoes.