Butterfly the steaks by slicing them horizontally from 1 long side to within 1/2-inch of the opposite side. Pound the steaks between plastic wrap to flatten them further. Trim off all the sinew and fat.
Lay 1 steak cut side up on a jelly-roll pan. Sprinkle the steaks with the vinegar, garlic, and thyme. Cover and marinate, refrigerated, for 3 hours.
Preheat oven to 375 degrees F.
Lay the steaks end to end, in the direction of the grain of the meat, so that they overlap. Pound the overlapping area to join them securely. Spread the spinach leaves evenly over the meat and arrange the carrots across the grain of the meat in parallel rows about 3 inches apart. Place the eggs between the carrots. Scatter the onion rings over the meat, sprinkle with parsley, salt, and pepper.
Carefully roll the matambre with the grain, jelly roll style, into a thick long cylinder. Tie with butcher's twine at 1-inch intervals. Place the matambre in a large casserole or roasting pan along with the beef stock. Add enough cold water to come a third of the way up the roll. Cover tightly and bake 1 hour.
Serve warm or chilled, sliced into 2-inch thick slices.