Heat 1 Tbs. oil in large pot over medium heat. Add mushrooms and garlic; sauté 8 minutes, or until mushrooms are browned.
Add remaining 1 Tbs. oil to pot. Add leek, and cook 5 minutes. Add potatoes, carrots, and tomato paste. Cook 2 minutes. Add tomatoes, broth, barley, cabbage and thyme sprigs; bring to a boil. Reduce heat to medium-low, cover, and simmer 40 minutes, stirring occasionally.
Add lager and simmer 10 to 15 minutes, stirring often. Remove from heat, stir in miso paste. Remove bundled thyme and stir in chopped thyme and parsley, and season with salt and pepper, if desired.