Combine diced steak and marinade ingredients in a large bowl or zip-top bag. Leave to marinate for 30 mins.
To make the salad, whisk together oil, vinegar, and a pinch of salt and pepper in another large bowl. Add cabbage and onion and stir to coat well with dressing. Toss through tomatoes, cucumber, and mint just before serving.
Thread marinated meat onto skewers and sprinkle with a bit of salt and pepper. Pre-heat BBQ or a large heavy-based skillet to medium-high.
Cook skewers 4–5 mins, turning to sear all sides. Transfer to a clean plate and cover loosely with foil and rest for 5 mins.
Serve skewers with warmed Lebanese bread, dips, and cabbage salad.