In a glass bowl, mix the oil, tamari, vinegar, lemon juice, mustard, garlic, and ground black pepper. Place meat in a shallow glass dish. Pour marinade over the steak, turning meat to coat thoroughly. Use fork to perforate both sides, with emphasis on the fat covering side. Cover, and refrigerate for 8 hours, or longer if you can, up to 24 hours.
Add the veggies into the marinade about an hour before grill time.
Pull out veggies from dish, let rest in a strainer for 5 minutes, then place in foil. Roll and seal the edges tightly
Preheat grill for medium-high heat
Put veggies on slow coals or on low part of grill in foil pouch.
Check veggies in 15 mins. If steamy and a little soft, pull to an area where they will stay warm but not hot.
Oil the grill grate.
Place steak on grill; brush marinade on while turning steak 3x, over about 8 minutes.
Let steak rest for 2 minutes on warm plate; place on cutting board and cut in thin slices across the grain, about 1/8” thick. We like these served fajita style, placing meat, pouched veggies, fresh salsa, greens, sour cream, and guacamole into tortillas (our gluten-free family uses rice flour tortillas).