In a small bowl, combine shiitakes and 1 1/2 cups boiling water. Let stand until softened, about 20 minutes, then remove mushrooms, reserving liquid. Trim stems from mushrooms and coarsely chop caps. Strain liquid through a fine-mesh sieve or coffee filter into a small bowl.
Heat oil in large saucepan or Dutch oven over medium heat. Add onion and garlic and sauté at least 5 minutes or until onion is golden. Add carrot and parsnip and sauté 5 minutes or until carrot is crisp-tender.
Stir in cabbage and cook, covered, 5 minutes or until beginning to wilt. Stir in 3 cups water, mushrooms, soaking liquid, lima beans, dill, tomato paste, vinegar and salt. Bring to boil, then reduce heat and simmer, covered, 25 minutes or until mushroom and winter vegetable soup is richly flavoured.