Combine the lamb, grated onion, garlic, cumin, coriander, paprika, cinnamon, salt, pepper, parsley and egg in a 4-quart / 3.8 L mixing bowl. Mix with your hands for about 1 minute, until the meat looks tacky and the spices are evenly spread.

Divide the mixture into 8 portions of about 90 g each. With wet hands, press each portion firmly around a flat metal skewer into a log about 12 cm / 4.75 inches long and 2.5 cm / 1 inch thick. Set them on a parchment-lined tray and refrigerate for 30 minutes. Don't skip this, because unchilled kebabs slide off the skewers.

While the kebabs chill, stir together the full-fat plain Greek yogurt, 2 tbsp chopped mint, 1 tbsp lemon juice, grated garlic, 1 tbsp olive oil and 1/4 tsp salt. Slice the cucumber, halve the tomatoes, and arrange them on a serving board with the olives, feta and lemon wedges. Cover and refrigerate the board and the yogurt.

Heat a 30 cm / 12-inch cast-iron grill pan over medium-high heat for 3 to 4 minutes, until a drop of water sizzles off it. Brush the ridges with half the avocado oil. Lay 4 kebabs on the pan with about 2 cm between them and grill for 8 to 10 minutes, giving each a quarter turn every 2 to 3 minutes, until deeply browned and 160 F / 71 C in the center.

Move the first batch to a plate and tent loosely with foil. Brush the pan with the remaining oil and grill the second batch the same way.

Let the kebabs rest for 3 minutes. Spoon the mint yogurt into a bowl on the board, drizzle 2 tbsp olive oil over the cucumber and tomatoes, scatter the remaining mint leaves on top, and serve the kebabs right away.