Preheat the oven to 400 degrees. Cut the top off the bulb of garlic, exposing the tops of all the garlic cloves. Place the bulb of garlic on to a sheet pan. Drizzle the top with about 2 teaspoons of olive oil and a pinch of salt and pepper.
Roast the garlic at 400 degrees for about 30-40 minutes, until the garlic is very soft and very brown. Remove from the oven and set aside.
While the garlic is roasting, cut the mushrooms into large chunks, I usually quarter mine. Then chop the carrots.
When the garlic is close to being ready, heat the remaining 1 tablespoon of olive oil in a large soup pot on medium high.
Then add the mushrooms and carrots, saute, reducing heat as needed, until the mushrooms have released their liquid and are starting to brown. Season with a pinch of salt and pepper.
Next, when the garlic is ready, squeeze all of the roasted garlic cloves out of the peel and into the pot with the mushrooms and carrots. Stir to combine.
Now, pour the vegetable broth, soy sauce and apple cider vinegar into the pot. Stir to combine. Then add the dried thyme and dried rosemary.
Bring the stew to a simmer, then pour the barley into the pot. Season with another pinch of salt and pepper. Continue to simmer on medium low until the barley is cooked. Check the package for timing. I like to use parboiled barley, which only takes 10-15 minutes, but regular barley takes about 30-45 minutes.
Once the barley is soft, taste the stew and adjust seasoning. Serve immediately with fresh herbs on top if you want.