When ready to cook the beans, drain and add the beans to a large pot. Add 4.5 quarts of water; you will be using the bean cooking liquid as the base for the soup, so you want plenty of water here. As you bring the beans and water to a boil, clean the various ingredients used to cook the beans listed above and add to a large soup sock and/or a spice bag. (You can leave the bay leaves out if you’d like and just add to the bean liquid, since you can continue using those for the final product too.)
Once the beans reach a boil, cover and set a timer for 10 minutes. When time is up, bring the mix down to a low simmer and cook, covered, for 30 minutes, or until beans are nearly cooked. (They can be just a little undercooked, since you will continue to simmer.) If the beans get overcooked, quickly remove from the heat, salt the water well, and add the tomotoes. The salt and acid will slow the cooking.
While the beans cook, prepare the other ingredients. Large dice the onion, mince or crush the garlic, and slice the celery and carrots into stew-worthy small pieces. For the celery, I usually slice the stalk in half vertically (or even fourths for very large stalks) and then slice into 1-2 cm slices. For carrots, I would cut large ones in half and then slice the halves (or smaller carrots) to 1-2 cm slices. Add all of the vegetables to a single large prep bowl. Rinse the pearled barley. Rinse the spinach.
Optional: If you are cooking the final soup in the same pot as the beans, you can wait until the beans are fully cooked and move the beans and their cooking liquid to a bowl to the side. Remove the soup sock and/or spice bags from the beans and their liquid. DO NOT DRAIN - you want to save all liquid.
Either way, in a large pot, add 2 tbsp of olive oil and heat over medium-high. Add the onion, garlic, celery and carrots. Add about 1 tsp salt and ½ tsp pepper (or to taste). Cook until they are softening and developing flavor, usually 5-7 minutes. It’s OK if the onion is taking on some color. Then, add the 2 tbsp miso paste or the 2 tbsp tomato paste. Cook until fragrant, 30-90 seconds. Add the can of tomatoes, with their liquid, and mix well. Season with the remainder 1 tsp salt and additional ½ tsp pepper (or to taste) remembering tomatoes soak up a lot of salt usually.
Add the rinsed 1 cup barley and the beans and their cooking liquid. Stir everything together. Lower the temperature once you’ve reached a simmer and allow to simmer for 30 minutes, until the barley is chewy and no longer hard.
Once the barley is cooked, add the rinsed spinach and turn off the heat. Add salt and pepper to taste.