Preheat the oven to 180°C.
Carefully wash the aubergines and cut them into thin slices lengthwise.
Place the aubergine slices in a greased oven dish. Cook for 5 minutes on each side and set aside.
Thinly slice the onions and garlic cloves and cook in a frying pan for 5 minutes on a low heat.
Add the minced beef, salt, cinnamon and oregano and then pour the tomato purée on top. Mix.
Dilute the cornflour with a little cold milk and heat the rest of the milk in a saucepan. When the milk is hot, add the cornflour and whisk it until it thickens. Season with salt and pepper.
Arrange the aubergines in the bottom of an oven dish, then add a layer of minced meat. Continue layering like this. Finish with a layer of aubergine and pour the cornflower/milk mixture on top. Sprinkle with grated cheese.
Put under the grill to brown in the oven for 20 minutes and serve immediately.