Place eggplant slices on a cooling rack over the sink, liberally coat the tops with kosher salt, wait 15 minutes, then turn and repeat. Let sit for 3 hours or more, then rinse off the salt, squeeze each piece like a sponge, then wrap in paper towels to dry.
Whisk together the oil, Worcestershire, vinegar and steak sauce in a bowl, season to taste, coat the eggplant with the sauce.
Broil until edges start to brown (about 3 minutes), then flip and repeat. Remove from broiler, sprinkle with Parmesan cheese, then return to broiler until the cheese is crusty.