Place the eggplant slices on a wire rack set over the sink. Sprinkle generously with kosher salt on one side, allow to sit for 15 minutes, flip, sprinkle, and allow to sit for another 15 minutes. Rinse thoroughly under cool water and gently squeeze out excess water. Place the slices on paper towels and pat dry.
Set an oven rack in the top third of the oven and heat oven to high broiler setting.
Whisk together the Worcestershire, steak sauce, olive oil, honey, and apple cider vinegar in a large bowl. Season with salt and pepper.
Place the slices in the bowl with the sauce and toss to coat. Transfer the eggplant slices to a half-sheet pan fitted with a wire rack. Place the tray under the broiler until eggplant is nicely browned, 3 to 4 minutes. Turn slices over and place back under the broiler until well browned, about 3 minutes. Generously sprinkle the Parmesan over all of the slices. Place back under the broiler for 1 minute to nicely brown the cheese. Serve plain or sprinkle with chopped parsley. Serve immediately.