Begin by heating your grill to its highest setting to ensure a perfect golden finish later. In a deep, ovenproof frying pan, brown the 500 g of beef over high heat for about 5 minutes. This step develops rich, caramelized flavors essential for the dish. While the beef cooks, prick the large aubergine all over with a fork — this helps it soften evenly — then microwave it on high for 3 to 5 minutes until tender. This quick cooking method speeds up the process without sacrificing texture. In a separate bowl, whisk together 150 g of Greek yogurt, one beaten egg, and 3 tablespoons of Parmesan cheese. Season lightly with salt and pepper to balance the tangy and savory notes. Once the beef is browned, mix in the 400 g of tomatoes, 4 tablespoons of tomato purée, and 350 g of potatoes. Add some seasoning to taste and stir well to combine. Heat this mixture through until the potatoes start to soften. Smooth the beef and vegetable mixture evenly in the pan using the back of a spoon for an even layer. Slice the cooked aubergine into rounds and neatly arrange them on top, covering the meat layer completely. Pour the yogurt, egg, and parmesan topping gently over the aubergines, spreading it out to create a uniform layer. Place the pan under the hot grill and cook until the topping is set and beautifully golden—this should take about 5 to 7 minutes. Tip: Keep a close eye on the grill as the topping can brown quickly. You can also swap microwaving with roasting the aubergine if you prefer a more caramelized flavor. Enjoy your delicious Moussaka warm, fresh from the grill!