Pickle the beets e.g. as in this recipe. Pour water into a large pot, add peeled and chopped carrot, parsnip, rinsed onion, leek, parsley. Bring to a boil, reduce heat to minimum and cook covered for about 45 minutes on minimum heat.
Remove vegetables from the broth (they won't be needed) and add the contents of the jar (pickled beets together with juice). Add marjoram, peeled and chopped garlic, apple juice, pepper, sugar, olive oil and salt to taste. Mix and bring to a boil on very low heat. Keep the soup this way uncovered on low heat for about half an hour, the soup should only heat gently, it must not boil. Strain into a clean pot, if necessary add more broth and heat. Serve with ear-shaped dumplings.
Rinse the mushrooms thoroughly under running water, place in a saucepan, cover with warm water and set aside to soak overnight (or faster - pour hot water and set aside for a few hours or as long as we have time). Add peeled vegetables to the mushrooms and water: carrot, parsnip and small onion, season with salt and bring to a boil, if necessary add a little more water. Cook on low heat covered for about 1 hour or until vegetables and mushrooms are soft. Towards the end add allspice and bay leaf. Cool.
Remove mushrooms and vegetables from the water, discard the onion. Press the mushrooms thoroughly in your hands, set aside. Rinse the sauerkraut twice under running water, place in a pot, cover with a small amount of water (to cover) and bring to a boil. After 5 minutes of cooking, taste the water and sauerkraut and if they are very salty, drain and pour in fresh water. Salt the sauerkraut and cook for about 40 - 50 minutes until it becomes soft. Cool and press in your hands like the mushrooms.
Pass the mushrooms, sauerkraut, carrot and parsnip through a meat grinder on the largest holes. We can also finely chop the mushrooms and sauerkraut with a knife, grate the vegetables on a grater. Place everything in a bowl. Add the onion sautéed in oil (about 8 minutes) finely chopped large onion, then season with salt, pepper, knead well by hand.
Prepare pierogi dough. Roll out the dough piece by piece into large flat cakes, cut circles with a small glass, place a small teaspoon of filling in the center, fold the dough in half, seal the edge and wrap around your finger connecting the two ends in one place, turn out the "ear". Drop the ear-shaped dumplings into salted and vigorously boiling water in a large pot and cook in batches (about 20 pieces) for about a minute counting from when the dumplings float to the surface. Remove with a slotted spoon and arrange on trays or plates keeping spaces between them. After cooling can be frozen (first on a tray then transfer to a bag) or keep in the refrigerator for up to 3 days. Reheat before adding to beet soup.