Purée the onion in a blender or food processor. Add the garlic, basil, salt, and pepper and pulse a few times to combine. Process in the vinegar. Pour the marinade over the flank steaks in a nonaluminum container; rub the marinade into the meat. Cover and let stand 2 to 3 hours at room temperature.
Heat a grill or broiler. Sprinkle the steaks lightly with salt and pe