Pat the beef dry with paper towels and season with the kosher salt and black pepper.
Heat the olive oil in a large Dutch oven over medium-high heat. Brown the beef in batches for 3 to 4 minutes per side until a deep golden crust forms. Transfer the beef to a plate.
Reduce the heat to medium. Add the onion, carrots, celery, and mushrooms, if using. Cook for 8 to 10 minutes, stirring occasionally, until the vegetables soften and the mushrooms release and evaporate their moisture.
Stir in the garlic and cook for 30 seconds. Add the tomato paste and continue cooking for 1 to 2 minutes, stirring constantly, until the paste darkens slightly.
Pour in the red wine, if using, scraping up all the browned bits from the bottom of the pot. Simmer for 2 to 3 minutes.
Return the beef and any accumulated juices to the pot. Add the beef broth, diced tomatoes, thyme, rosemary, marjoram (if using), bay leaves, and Worcestershire sauce. Bring to a boil, then immediately reduce the heat to a gentle simmer.
Cover and simmer for 60 minutes.
Stir in the pearl barley. Continue simmering uncovered for 30 to 35 minutes, stirring occasionally, until the barley is tender and the beef is fork-tender.
Stir in the frozen peas during the last 5 minutes of cooking, if using.
Remove the bay leaves. Stir in the vinegar or lemon juice, butter (if using), and 1 tablespoon of the chopped parsley. Taste and adjust the seasoning with additional salt and pepper as needed.
Let the soup rest for 10 to 15 minutes before serving.
Garnish each bowl with the remaining parsley and serve warm with crusty bread or dinner rolls.