DO-AHEAD TIP: Marinate steaks overnight (see recipe).
Place steak in a large zipper-topped plastic bag; pour teriyaki sauce over steak then seal bag and turn to coat.
Refrigerate overnight, turning occasionally.
At time of cooking preheat grill to MEDIUM-HIGH. In a large bowl, combine olive oil, Italian seasoning, salt and pepper. Add mushrooms, bell pepper and onion; toss to coat thoroughly.
Place marinated beef on the grill first--it needs 5 to 8 minutes per side, depending on thickness and desired level of doneness.
Remove steak from the grill to a cutting board and allow it to rest for 10 minutes.
Next, add vegetables to the grill, using a grill basked or tray; grill until veggies are lightly charred, 5 to 6 minutes, turning occasionally; remove from grill and keep warm.
Thinly slice steak against the grain (diagonally) and serve with grilled veggies.