Cut the aubergines in half lengthwise. Spoon out the flesh without damaging the skins. Leave about a 3mm of the walls.
Roughly chop the flesh with a knife, sprinkle generously with coarse salt and let stand for 20 minutes. Rinse well to remove salt and squeeze out extra liquid.
In a saucepan add 200ml oil and fry the garlic, onion and the parsley stems on medium heat. Add a dash of wine to avoid burning and cook for 3 to 4 minutes, stirring. Add the aubergine flesh and stir to coat in oil. Cook for 15 minutes, stirring from time to time. Remove from heat and set aside to cool slightly.
Meanwhile, heat about 1 cm oil in a saucepan. Add the aubergine skins, a few at the time and fry them quickly, 1 to 2 minutes. Remove with a slotted spoon and drain on kitchen paper.
Transfer the aubergine flesh to a bowl and add grated Parmesan, eggs, squeezed and crumbled stale bread, parsley leaves, capers and olives. Season with salt and stir well. Fill the aubergine skins with this mixture.
Preheat the oven to 200 C / Gas 6.
Pour 2 ladles of tomato sauce on the bottom of a baking pan and lay the stuffed aubergines, one close to the other. Add more tomato sauce and sprinkle with grated pecorino cheese.
Bake in the preheated oven for 30 minutes. Move to the top oven shelf during the last minutes to brown the top.
Remove from the oven, let it cool slightly and serve. This dish is better if prepared some hours in advance or even the day before.
Store the stuffed aubergine in the fridge up to 2 days. Freeze up to 3 months.