Heat the oil in a large pot over medium heat. Add the onion and sauté for 5 minutes, or until translucent. If not using oil, just sauté with broth.
Reduce the heat to medium-low. Add the barley, garlic, and thyme and sauté for 3 minutes.
Stir in the mushrooms. Add the broth, tomato paste, vinegar, miso, bay leaf, and 1/4 teaspoon salt and stir to combine. Bring the soup to a boil. Reduce the heat to low, cover, and simmer for at least an hour, or until the barley is tender. Note that this only took about 25 - 30 minutes for me to get the texture I wanted. (If using sorghum, it will be soft but slightly chewy once cooked.)
Remove the bay leaf. Season to taste with more salt, if desired, and black pepper.
Store leftover soup in an airtight container in the refrigerator for up to 2 days.
I easily made this oil free by sautéing with broth.
I used chickpea miso and it worked great, it also kept it soy free.
I did not need to simmer this for an hour, it was ready in about 25 minutes for me. We like our barley more on the al dente side however.
I added a few handfuls of spinach to this, it gave it some greens and went really well with the flavors!