Arrange steaks in a single layer in a shallow nonreactive dish. Whisk together remaining ingredients, and pour over steaks. Cover, and marinate in the refrigerator, flipping occasionally, for at least 6 hours (or up to 2 days).
Preheat grill to medium-high. (If you are using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for just 3 to 4 seconds.) Transfer steaks to plates, and pat dry; reserve marinade. Season steaks generously with salt and pepper. Cook over direct heat (the hotter part of the grill) until browned and caramelized, about 4 minutes per side, then move to indirect heat (the cooler part of the grill) and continue cooking until a meat thermometer registers 135 degrees for medium-rare, about 5 minutes more. Transfer to a platter, cover, and let rest, 10 to 15 minutes.
Bring marinade to a boil in a saucepan; let boil 5 minutes. Pour over steaks, or serve on the side. Season steaks with salt and pepper. Serve with chimichurri and aioli, and garnish with bay leaves, fresh chiles, oregano, and bell pepper.