Peel and cut the potatoes and carrots into medium-sized pieces to be able to mash them. Boil them in salted water (large pot). Shortly before they're fully boiled, add the finely chopped mushrooms, margarine and broth cubes.
Once the mushrooms are cooked, remove from the heat and blend them. Allow to cool and add the milk, stirring constantly, and the tomato paste diluted with some water. Put back on the heat and reduce the heat to medium, stirring often.
After 10 minutes, add the dill and black pepper, then after another 2-3 minutes, remove from the heat.
Pour in the egg white, beaten lightly in advance, while stirring constantly. The soup can be served with toast or croutons, it can also be consumed cold.