Preheat the oven to 200 °C. Cut the eggplant lengthwise into 2 cm thick slices . Brush them with butter and salt. Place on parchment-lined baking sheets in one layer and place in the oven. Bake until soft and browned, about 20 minutes.
Peel thyme and rosemary from the stalks, chop the leaves together with garlic and salt as small as possible. Mix with 3 tablespoons of olive oil.
Pour boiling water over the tomatoes, put them in cold water for 1 min., remove the skin. Cut the tomatoes into 2 cm thick slices .
Brush a deep rectangular baking dish (preferably ceramic) with plain olive oil. Put the eggplant and tomatoes in layers in a mold, sprinkling with olive oil with herbs and garlic.
Having laid out half of the products, cover them with a layer of slices of melted cheese. Put the remaining cheese on top.
Place the mold in the lower third of the oven, bake for 20 minutes. Serve the dish very hot.