Heat 1 tsp avocado oil in a large soup pot over medium heat. Add vegan steak bites and cook until lightly browned, about 5 minutes.
Add another tsp oil, yellow onion, carrots, celery, minced garlic, and a pinch of salt. Sauté for 5 minutes until softened and fragrant.
Stir in dried marjoram and thyme, cooking for 30 seconds until aromatic.
Pour in red wine, scraping the bottom of the pot to loosen any browned bits. Cook for 3 minutes until reduced.
Add water, Better Than Bouillon no beef base, vegan Worcestershire sauce, tomato paste, pearled barley, and bay leaves. Stir, bring to a simmer, then cover and cook for 35 minutes until barley is tender. Add potatoes with 20 minutes left, green beans with 15 minutes left, and peas with 3-5 minutes left.
Once barley and potatoes are tender, turn off heat, remove bay leaves, and ladle into bowls.