Put the onion and garlic in a food processor and whizz to a very fine pulp. Transfer to a sieve lined with a clean J-cloth and set over a large bowl. Bring the cloth around the pulp and squeeze to extract as much juice as you can (it’s best to wear rubber gloves for this, to protect your hands from the smell). Discard the pulp (or save for a tomato sauce base), then mix the juices with the turmeric, tomato purée, yogurt (or milk), paprika and salt. Add the chicken and coat well. Cover and marinate for at least 1 hour or up to 24 (see Make Ahead).
If you’re using wooden skewers, soak them in cold water to stop them burning. Heat the grill to as high as it will go. Thread the chicken onto 4-8 metal or wooden skewers, depending on how long they are. Line a baking tray with foil and drizzle with a little oil, then lay the chicken skewers on top. Grill for 10 minutes or until the chicken is blackened and completely cooked through (no need to turn it). Scatter with oregano and sumac, then serve immediately with your choice of accompaniments.