Wash the aubergines, cut them into slightly thick slices and pre-cook them for 10 minutes in steam or in the microwave (with a little water in the dish).
Preheat the oven to 240°C.
Put a little oil in a dish that can hold the rib and place it in the oven for 5 minutes.
Place the rib in it and cook it for 20 to 25 minutes depending on its weight, turning it every 5 minutes. (you can also cook it in a pan or on the barbecue).
Peel 2 cloves of garlic and chop them with the parsley.
Meanwhile, brown the eggplants in a large nonstick skillet with olive oil over medium heat, turning them regularly.
At the last moment, sprinkle with chopped parsley and garlic.
For the pesto:mix the basil with the 3 cloves of fresh peeled garlic, the olive oil, salt, pepper, set aside.
Let the meat rest for 5 minutes wrapped in aluminum foil, before carving it.
Serve it topped with the pesto sauce and a few drops of balsamic vinegar with the grilled eggplant.