Salt the eggplant slices lightly inside a mixing bowl. Heat 2 to 3 tablespoons of the olive oil in a large, heavy skillet over medium-high heat and lightly brown the eggplant slices on both sides, in batches, replenishing the olive oil if necessary. Drain on paper towels.

Preheat the oven to 350F/170C.

In the same frying pan, add the garlic and cook gently for a few minutes, just to soften. Add the tomato, cook it down a bit over medium heat, season with salt and pepper to taste, and add the honey and vinegar. Simmer gently until thick, about 15 to 20 minutes.

Place a few tablespoons of the sauce on the bottom of a medium sized baking dish and drizzle in a little olive oil. Place the eggplant slices on top, sprinkling with herbs and a little cheese, if desired. Spread a little sauce over the eggplant and continue layering in the same manner until everything is used up. Press down with a spatula and sprinkle a little vinegar on top. Bake for about 45 minutes, remove, sprinkle with chopped parsley and serve, with creamy polenta or feta, or both.