Place barley in a sieve and rinse it thoroughly under water. Transfer it to a bowl, cover with 2 cups (480ml) of water and let soak for 30 minutes. Meanwhile prepare all the vegetables.
In a large pot heat olive oil over medium-high heat. Add onions and cook until tender (takes a few minutes, some browning is okay). Stir in tomato paste and let it cook for 1 minute. Toss in the carrots, leeks, and celery. Cook until leeks are softened, then add the garlic, potatoes and parsley. Stir the vegetables a few times and cook for about a minute, until the garlic is aromatic.
Add the soaked barley along with the water, diced tomatoes and 3 cups vegetable stock. Stir until evenly distributed and make sure all potatoes are submerged. Bring to a boil, then lower the heat to medium and cook covered for about 40-50 minutes, until the potatoes are soft and barley tender.
Stir soup occasionally as it cooks and check to see if it’s simmering.
Turn off the heat and fold in the beans. Taste to see if the soup needs more salt or pepper. Add more vegetable stock if it's to thick for your liking. Sprinkle with some parsley (optional) and serve.Store leftover soup in the refrigerator for up to 2 days or freeze it for up to 3 months.