Place the ribeye pieces in a bowl, add the olive oil, yogurt and black pepper. Combine and make sure all pieces are coated with the marinade. Cover and refrigerate for 4 to 8 hours.
When you're ready to grill, take the meat out of the fridge and let it come to room temperature. This is to make sure the meat cooks evenly. Thread them on flat skewers that are about 1/2 inch wide. Thread the tomatoes separately.
Preheat the grill to medium high. If using charcoal grill, you want to make sure that the charcoals have stopped smoking, are glowing uniformly and there's a layer of ash on them.
Place the skewers on the grill and cook for a couple of minutes, flip and cook on the other side. It takes the kebabs 4-5 minutes on each side (flipping a few times) to grill completely. Keep an eye out so you don't overcook them. It'll take the tomatoes about 15 minutes to cook completely, the skin will be charred, don't worry we're going to discard the skin before serving.
Once the kebabs are almost ready, season them with kosher salt. Mix the melted butter and bloomed saffron and brush it on both sides of the kebab. This is to keep the meat juicy and tender.
Transfer the cooked kebabs to a pot with lid so they stay warm. You can use a piece of lavash to remove the kabob pieces from the skewers.
Serve with lavash, rice and sabzi khordan.