Place the beef in the brine and leave, covered, for 1 hour.
Drain and transfer to a clean bowl. Add the extra virgin olive oil, garlic, chilli, lemon zest and thyme, then leave to marinate for at least 1 hour.
Light the barbecue and set for direct/indirect cooking.
Remove the beef from the marinade, season with salt and pepper and place on the grill in the direct heat zone. Keep a close eye on the steaks: bavette cooks quickly as it is quite thin, and it shouldn’t be cooked past medium-rare otherwise it’ll be tough. Grill for 2 minutes on each side to char, then move to the cooler edge of the barbecue to rest for a couple of minutes.
Cut the onions in half lengthwise, keeping the stalks intact. Toss them with a little olive oil, season with salt and pepper and place directly on the grill in the direct heat zone and cook for 3–4 minutes until charred and tender.
Thickly slice the steaks and serve with the grilled onions and salsa cruda.