1. Whisk together the Worcestershire sauce, soy sauce, brown sugar, mustard, vinegar, garlic, black pepper, medium bowl and whisk until smooth. Remove 2 tablespoons of the marinade and set aside in a small ramekin. Whisk in the oil.
2. Place the flank steak inside a gallon-sized zipper-lock bag with remaining marinade. Press out air, seal the bag, and allow meat to marinate, turning occasionally, for at least 4 hours and up to 24 hours.
3. Prepare the grill for direct grilling over a medium-high fire ( 600°F) with an indirect cooking zone as well. A charcoal fire is preferred. Remove the flank steak from the marinade and blot dry with paper towels. Brush both sides with a bit more avocado oil and season with a bit more salt and pepper.
4. Grill the steak over direct heat until charred on both sides, 60 to 90 seconds per side. Move the seared steaks away from the direct fire to the indirect side, close the lid, and gently roast them until they reach your desired internal temperature (such as 125 for medium-rare), turning every 90 seconds.
5. Transfer the meat to a cutting board, loosely tent with foil and let rest for 10 minutes. Slice thinly against the grain making sure to pour any of the accumulated juices over the meat before you serve it!