Butterfly flank steak, slice half horizontally, toward the grain, within 1/2 inch of far lengthwise side (or ask your butcher to do it for you) so steak opens up like a book. Using meat mallet, pound opened steak until it is 1/4 inch thick.
In large bowl, combine vinegar, onion, garlic, chile, parsley, thyme, and 1 teaspoon of salt. Drop steak into mixture and rub well on all sides. Cover and refrigerate at least 4 to 5 hours or overnight.
Cut carrots in half lengthwise, then cut each halves into 4 lengthwise strips; set aside. Moisten breadcrumbs with milk, stir to make a granular mixture, set aside.
Preheat the oven to 350°F.
Drain steak, reserving marinade. Sprinkle 3 remaining teaspoons over opened steak and sprinkle breadcrumb mixture. Layer with spinach and arrange carrot slices over width of steak. Place egg wedges between carrot slices, and top with onion rings. Carefully roll steak jelly-roll fashion to cover filling completely. Secure steak with string tied at 1-inch intervals. Tie 2 pieces of string lengthwise along steak to secure further and keep intact while filling.
Place rolled steak in large baking dish or Dutch oven. Add 1 1/2 cups water, bay leaf, and reserved marinade. Cover well with foil or lid and bake for 1 hour. Uncover and bake another 10 minutes. Transfer to cutting board and let cool 10 minutes before cutting into 1/2- to 1-inch-thick slices. Serve moistened with cooking juices from pan.