Peel the eggplant. Slice very thinly into circles, about 1/8-inch thick - a mandolin or electric slicer produces the best results. In a bowl, submerge the slices in milk and add a big pinch of salt and half of the thyme. Cover and soak overnight, or for at least two hours.
Drain the milk and dry the eggplant slices on paper towels. Dredge in flour (seasoned with another pinch of salt and a few turns of black pepper if desired), then fry in hot oil until golden brown. (Fry in batches so as to not overcrowd the pan.) Remove the eggplant and drain on paper towels.
Arrange slices on serving plates or platter, drizzle lightly with honey and sprinkle with sea salt and the reserved thyme. Serve immediately.