For the Marinade
Add the first four ingredients to the bowl of a food processor. Whirl, scraping down the sides of the bowl, until well blended and the cilantro is just shy of smooth. Place the Bavette steak in a one-gallon zip-lock bag and pour in the marinade. Place in the refrigerator and allow to marinate at least one and not more than four hours, turning and smooshing the bag occasionally to distribute the marinade.
Prep the peppers and onions and set aside until time to grill.
Heat a gas grill to high (about 500°) and let the grates get very hot. For a charcoal grill, build a bed of charcoal large enough to cook your grill pan of vegetables and the steak over hot direct heat. Place the grill pan on the grates while the grill heats.
Start the vegetables first: Spray your hot grill pan with cooking spray (stand back and be very careful to avoid flames) and scoot all the vegetables into it. Do not disturb the vegetables for 2-3 minutes to allow some charring before turning them. Do this several times throughout the cooking to get a nice char without overcooking the vegetables. depending on the heat of your grill, the size of your grill pan, and the amount of vegetables, this can take 10-20 minutes.
When the vegetables are about 5 minutes from being ready, spray the grates where the meat will cook, and place the meat on the grill. Again, do not disturb the meat to allow for great charring. After 2-3 minutes, check for char and flip. Repeat on the second side. It is very easy to overcook this thinner cut of meat, which may render it tough, so again, err on the side of caution.
While the meat is resting, heat a skillet to medium-high. Toast the tortillas until they are warm, soft, and beginning to blister, flipping once, about a total of 1 minute each. Slice the steak thinly across the grain. Pile peppers and onions and sliced steak into the tortillas and top with the avocado-tomatillo salsa. Serve!