In a large pot, heat the olive oil over high heat and sauté the chopped onion until soft and transparent.
Add the carrots, garlic, tomato paste, and bay leaf, then sauté for about 5 minutes.
Add the green peas and corn, and sauté everything for another 8 minutes.
Pour in the vegetable broth and water, and bring the mixture to a boil.
Add the pearl barley, potatoes, and red kidney beans. Bring the soup to a slow boil.
Simmer the soup for 30-40 minutes or until the pearl barley is fully cooked. If the soup becomes too thick, add another cup of water as needed.
Add the spinach or kale (if using) and simmer for another 10 minutes. Adjust seasoning to taste.
Serve the soup with a dollop of vegan sour cream, a wedge of lime, and warm flatbread.