In a small saucepan, reduce vinegar to low heat and keep warm.
Peel the carrots by keeping their tops, wash them, drain them and cook them in the broth. Drain and keep warm.
Place the eggplants, a branch of thyme and a bay leaf on a large sheet of aluminum foil: salt, pepper and drizzle with olive oil.
Train and close the foil. Bake and bake for 45 minutes (180 ° C – Th.5).
Remove the foil and allow it to cool.
Slice the eggplants and, with a spoonful, recover their flesh, mix it and sieve it, then correct the seasoning.
Using the 2 tablespoons, make beautiful quenelles and keep them warm.
Clean (without washing) and slice mushrooms. Steam with olive oil, salt and pepper.
In the casserole, brown the meat with a touch of olive oil, 1 sprig of thyme, 1 bay leaf and the cloves of garlic. Salt and pepper on all sides. Add the dried tomatoes.
Discovered, put the casserole in the oven for 7 minutes (220 ° C – Th 8).
Once cooked, let the meat rest for a few moments before serving sliced, accompanied by tomatoes, mushrooms and quenelles of aubergine caviar generously drizzled with caramelized vinegar.
Serve with a green salad.