Peel the black radishes. Slice one into thin rings and finely grate the other.
Combine the honey with 1 tablespoon of water in a sauté pan. Bring to a boil, add the sliced radish rings, stir well, and simmer for 10 minutes over low heat, stirring occasionally until glazed.
Heat the frying oil in a saucepan and fry the grated radish for 2 minutes. Drain on paper towels, season with salt, and set aside.
Wash and dry the apples. Core them using an apple corer, then slice into 1 cm thick rounds. Melt the butter in a frying pan and brown the 12 best apple slices (2-3 minutes per side).
Cut the foie gras into 8 slices. Lightly dredge in flour, then sear in a hot non-stick pan for about 2 minutes per side until golden. Season with salt and pepper.
On each of 4 serving plates, arrange an apple slice, top with a foie gras slice, and finish with another apple slice. Surround with the honey-glazed radish rings, scatter the fried grated radish on top, and drizzle a few drops of balsamic vinegar over the radishes.
Serve immediately for the best texture and flavor.
