In a large pot (6 to 8 quarts), cook bacon over medium-high heat, stirring often, until crisp, 3 to 5 minutes. Reduce heat to medium.
Add onion and garlic; season with salt and pepper. Cook, stirring occasionally, until onion is starting to brown, 3 to 5 minutes. Add mushrooms; cook, stirring often, until they are tender and pot is almost dry, 5 to 10 minutes (depending on type of mushrooms). Stir in tomato paste, and cook 1 minute more.
Add broth, barley, oregano, and 3 cups water; bring to a boil. Reduce heat; simmer, partially covered, until barley is tender, 10 to 15 minutes. Add more water to thin soup, as needed. Season with salt and pepper, and stir in vinegar. Ladle into bowls; sprinkle with parsley.