Heat one tablespoon of the olive oil in a large heavy pot or Dutch oven over medium-high heat. Add half the cremini and all the shiitake in a single layer and cook, without stirring, for three to four minutes, until the undersides are deep golden. Stir, cook two minutes more, then transfer to a plate. Repeat with another tablespoon of oil and the remaining cremini. The mushrooms should be well browned and reduced in volume, not pale and steaming.

Lower the heat to medium and add the last tablespoon of oil. Add the onion, carrot, and celery and cook for six to seven minutes, stirring now and then, until the onion is soft and translucent and the edges just start to catch color.

Stir in the garlic and cook for thirty seconds, until fragrant. Add the tomato paste, soy sauce, thyme, and dried parsley, and stir constantly for about a minute so the paste darkens slightly and coats the vegetables. This step is what builds the savory base, so don't rush it.

Return the browned mushrooms to the pot along with the pearled barley, bay leaves, and vegetable broth. Stir well, scraping up any browned bits from the bottom, and bring to a boil.

Reduce the heat to low, cover, and simmer for forty minutes, stirring once or twice, until the barley is tender with a slight chew and the broth has thickened. If it looks too thick before the barley is done, add another half cup of broth.

Remove the bay leaves and stir in the lemon juice. Taste and season with salt and black pepper, keeping in mind that the soy sauce is already salty. Ladle into bowls and finish with fresh chopped parsley.