Preheat the grill to 350 degrees F (175 degrees C).
Drizzle steak with 1 tablespoon olive oil. Season with Italian seasoning, garlic powder, sea salt, and black pepper.
Lay eggplant out in an even layer on a wood board and lightly season both sides with salt.
Heat 2 tablespoons olive oil in a large cast iron pan on the grill. Add Brussels sprouts and eggplant. Cook until browned on all sides, flipping halfway, about 15 minutes.
Move vegetables to 1 side of the pan; add remaining olive oil. Turn the vegetable side of the pan towards the outer side of the grill where it it not as hot, keeping the open half of the skillet in the center of the grill.
Place steak in the hot pan. Cook until browned, about 3 minutes. Flip and continue grilling until the inside is to your desired doneness, 2 to 3 minutes more; for medium, an instant-read thermometer inserted into the center should read 140 degrees F (60 degrees C). Let rest briefly before serving.