Preheat your oven to 450°F (220°C) with the convection setting on.
In a large bowl, mix together the ground lamb, minced lamb fat, salt, cumin, and Aleppo pepper until well combined. The mixture should be cohesive and slightly tacky, with visible streaks of fat and pepper.
On a well-oiled half-size sheet tray, press the meat mixture into a uniform block. Use a spatula or bench scraper to cut kebap shapes directly on the tray.
Arrange the tomatoes and green peppers in the remaining spaces on the tray and drizzle everything with oil.
Roast in the oven with convection for 15 to 18 minutes, until the tomatoes, peppers, and kebaps are nicely charred.
Switch the oven to broil on the highest setting and broil for 1 to 2 minutes, watching closely to avoid overcooking.
In a bowl, combine the diced onion, chopped tomatoes, finely chopped red pepper, parsley, and salt. Mix well and then transfer to a strainer to drain excess liquid, concentrating the flavors.
Transfer the drained mixture to a serving bowl and dress with lemon juice, pomegranate molasses, black pepper, and olive oil. Toss and adjust seasoning as needed.
In another bowl, combine the sliced red onion, parsley, lemon juice, olive oil, sumac, and salt. Toss well and let it sit for at least 10 minutes to soften the onion.
To serve, take a piece of lavash and press it against the sheet tray to soak up the rendered lamb fat. Place the fat-soaked lavash on a plate as the base.
Top the lavash with several kebaps, a generous spoonful of the ezme salad, a pile of sumac onions, and a dollop of cold yogurt.
