4 slices hearty white or sourdough bread, for serving
In a medium bowl, add the boiling water and the dried mushrooms. Allow to soak for about 15 minutes, or until well-hydrated and softened. Retain the liquid after straining through a fine-mesh filter. Porcini should be roughly chopped and kept aside.
Over medium-high heat, warm the olive oil in a big pot or Dutch oven. Carrots, onion, cremini mushrooms, if using, 1/4 teaspoon salt, and several grinds of pepper should all be added. Cook for 8 to 10 minutes, stirring periodically, or until all the veggies are soft and the mushrooms are golden brown.
To the saucepan, add the tomato paste, 1 tablespoon of vinegar, and the garlic. Cook the mixture, as usual, scraping off any browned bits from the pan's bottom with a wooden spoon. Over the veggies, equally, distribute the flour and thyme, and simmer, stirring, for about a minute, or until the flour is dissolved and no longer raw. Add the porcini, broth, barley, leftover liquid from the mushrooms, 1/2 teaspoon salt, and several pinches of pepper. Bring to a boil, lower the heat to a simmer, cover loosely, and cook for 30 to 35 minutes, or until the barley is soft and the soup has slightly thickened and decreased.
Add salt and pepper to taste. Ladle the mixture into 4 dishes after adding the final 1 tablespoon of vinegar. Serve with a slice of bread for dipping and top with a dollop of sour cream and some fresh parsley.