For the dressing/marinade: Combine the oil, both vinegars, lime juice, soy, Worcestershire, chili oil, sugar, ginger, garlic, salt and pepper in a mason jar with the lid. Shake vigorously to combine; taste and adjust seasonings to taste.
Place the steak in a plastic zipper bag. Pour in half the dressing/marinade and seal. Marinade for 5 to 10 minutes.
For the onion strings: Slice the onions very thin. Place in a baking dish and cover with the buttermilk and soak. Combine the flour, salt, cayenne and black pepper and set aside.
Heat the oil to 375 degrees in a large pot. Grab a handful of onions, throw into the flour mixture, tap to shake off excess and plunge into the hot oil. Fry for a few minutes and remove to a paper-towel-lined plate as soon as they are golden brown. Repeat until onions are gone.
Grill (or saute) the steak over medium-high heat until medium-rare, about 2 minutes on each side. Remove from the heat and allow to rest. Slice the steak against the grain in thin slices.
For the salad: In a large bowl, add the lettuce mix, blue cheese and tomatoes. Add a little of the remaining dressing/marinade and toss to combine. Add more if needed.
Heap the salad on a plate, making sure to get plenty of blue cheese and tomatoes on each plate. Add half a steak to the top of each plate, then top the steak with onion strings.