Put the mushrooms in a small bowl, then cover with 1½ cups of boiling water. Let them stand for 15 minutes, or until rehydrated and softened. Remove the mushrooms from the soaking liquid with a slotted spoon, reserving the liquid. Trim and discard any tough stems from the mushrooms and roughly chop the caps. Strain the reserved liquid through a sieve and set aside.
Meanwhile, heat the oil in a large saucepan over a moderate heat. Add the onion and garlic and cook for about 5 minutes, stirring occasionally until the onion is light golden. Add the carrot and parsnip and cook for 5 minutes, then stir in the cabbage. Cover and cook for a further 5 minutes, or until the cabbage begins to wilt.
Stir in the mushrooms and the reserved soaking liquid, the beans, tomato paste, vinegar, 3 cups of water and the dill, if you are using it. Bring to the boil, then reduce to a simmer; cover and cook for 25 minutes until well flavoured. Season to taste with salt and pepper.