Cook the barley in a medium sized pot, according to package directions. It should take about 25 minutes. I prefer to cook the barley separately so it doesn’t soak up all the soup broth while it cooks. When the barley is done cooking, drain any excess water and set it aside for later.
While the barley is cooking, saute the diced onions in a few tablespoons of water or broth in a large soup pot or dutch oven over medium heat, until the onions are translucent. While the onions are cooking, add a pinch of salt. Then add the sliced mushrooms and minced garlic and let it cook until the mushrooms start to brown.
Add the sliced bok choy, ginger, mushroom broth, and water to the pot. Bring the soup to a low simmer and then quickly reduce the heat to medium-low and let it cook (about 5-8 minutes) until the bok choy has softened a little but try not to overcook it. The bok choy should still be bright green and it will be tender and easy to chew.
Take the soup pot off the heat. Carefully, use a measuring cup or ladle to remove one cup of the broth from the soup pot and put it into a small bowl. Let the liquid cool down for a few minutes and then stir in the miso paste.
Let the soup in the pot cool down a little bit (for about 5 minutes) and then stir in the miso paste broth that you just made, lemon juice, and roughly chopped fresh cilantro.
To serve the soup, put a 1/2 cup of cooked barley in each soup bowl and then serve the mushroom barley soup on top of it. The warm broth will help to break up the cooked barley and give it a stir to combine. Garnish each bowl with sliced green onions.