Peel eggplant and cut into slices half-inch thick. Place in a bowl. Sprinkle with salt and let stand for 30 minutes. Pat dry with paper towel. Dredge with flour.
In large skillet, heat 2 tablespoons butter. Add aubergine and cook over brisk flame for 10 minutes on each side, or until well browned. Remove eggplant to heated serving dish. Sprinkle with parsley. Keep warm.
Add remaining butter to skillet and cook until butter is slightly browned. Pour over eggplant. Serve very hot.