Cut the eggplants in 2 lengthwise, scoop them out, salt them and leave for 1 hour to release their bitter juice. Wash and dry them, fry on all sides in heated oil.
In the same oil, fry the finely chopped carrots, onions and insides of the eggplants. Add the grated tomatoes, garlic, salt, black pepper, parsley and bay leaf.
Let simmer on low heat until the water evaporates. Butter the tray you intend to bake in, pour some of the mixture at the bottom. Fill the eggplant boats with a few spoons of the mixture.
Arrange slices of tomato on top and bake at 356°F (180 °C) for 30 min. Sprinkle with chopped parsley and serve.