Preheat the oven to 300°F (150°C).
Pat the beef dry with paper towels and season it with salt and black pepper.
Heat 1 tablespoon of olive oil in a large Dutch oven over medium-high heat.
Working in batches, brown the beef on several sides. Add the remaining oil as needed. Transfer the browned beef to a plate.
Add the sliced onions to the Dutch oven. Cook for 4–5 minutes, scraping the browned bits from the bottom of the pot.
Return the beef and any accumulated juices to the Dutch oven.
Pour in approximately 1½ cups of tomato juice. The liquid should come about halfway up the meat.
Bring the tomato juice to a gentle simmer. Cover the Dutch oven and transfer it to the preheated oven.
Braise for 3–4 hours, checking the liquid after approximately 2½ hours. Add the remaining tomato juice or a little hot beef broth if the sauce becomes too thick.
The beef is ready when it is very tender and easily pulls apart with a fork. If necessary, continue cooking for another 30–60 minutes.
Remove the Dutch oven from the oven and let the beef rest, covered, for 10–15 minutes.
To prepare the optional salad, combine the red cabbage, carrot, mixed greens, and herbs. Dress with olive oil, lemon juice, and salt.
Serve the braised beef with its tomato sauce over mashed potatoes, rice, pasta, or polenta. Alternatively, serve it in warm pita with hummus and cabbage salad.