Combine the stew beef in a bowl with ½ teaspoon of sea salt, ¼ teaspoon of black pepper, and the all-purpose flour. Mix well and let sit for 10 minutes.
Heat 1 teaspoon of olive oil in a large pot and sear the beef until brown, about a minute per side. Sealing the beef in batches is best so the meat can brown properly. Transfer the seared beef to a bowl or plate.
In the same pot, heat 1 teaspoon of olive oil over medium. Add the onions, carrots, celery, and parsnips, and cook the vegetables until they have softened, about 6 minutes. Add the sliced leeks and cook until the leeks welt.
Stir in the minced garlic and cook until fragrant. Add a touch of sea salt and black pepper and stir well.
Add the beef broth and water. Gently scrape all the brown bits off the bottom of the pot. Return the seared meat to the pot, add the bay leaf, cover, and bring the soup to a boil. Once the soup reaches a boil, reduce the heat to medium-low. Simmer for 20 minutes.
Add the barley and cook until the barley is tender, about 15 minutes. Taste and adjust the seasoning with sea salt and black pepper. Serve hot.