In a big soup pot, heat the olive oil over medium heat. Throw in the onion, carrots, and celery and sauté it until everything is soft and started to turn golden, about 8 minutes. Add the garlic, mushrooms, 2/3 of the chopped roasted peppers, the rosemary, and the soy sauce and sauté until the mushrooms start releasing some of their moisture and look kind of cooked, about 5 minutes.
While that’s all cooking, throw 3 cups of vegetable broth in a blender with the remaining amount of roasted bell pepper and blend until it looks smooth. (In a hurry or hate extra dishes? Skip this step and just add the rest of this roasted pepper when you add the other roasted peppers in step 1.)
When the mushrooms have started breaking down, add the tomato paste, cooking for a minute or two to kind of caramelize it. Add the vinegar and barley and sauté for another minute. Add all the broth, including the one with the pepper in it, a pinch each of salt and pepper, and let that all simmer together over medium-low heat until the barley gets soft, 40-50 minutes.
Taste at the end and add more salt and pepper before dishing out. Serve with some chopped parsley on top.