Heat vegetable oil in a large cast-iron saucepan (cauldron) over medium heat. Place the chopped mushrooms in a saucepan and cook, stirring occasionally, for about 5 minutes. Add the onion to the cauldron and fry for about 6 minutes. Place celery, carrots, and parsnips in a saucepan and cook for about 4 minutes.
Then add tomato paste, 7 glasses of water, and beer, stirring, to a boil. Reduce heat and cook vegetables for about 5 minutes, stirring occasionally. Then put the shredded cabbage, potatoes, garlic, and beets in a saucepan, cook for about 20 minutes. Remove the pot from the stove.
Pour half the contents of the pan into a blender bowl and puree until smooth (this must be done with an open hole for steam to escape). Pour the puree into a large bowl. The remaining borscht from the saucepan is also mashed in a blender and the mashed borscht is poured into the same bowl. Add vinegar, sugar, salt, and pepper to the borsch-puree.
Pour about 1.5 cups of borscht-puree into each of 8 serving plates and add 1 tablespoon of sour cream and 3/4 teaspoon of dill to each serving. Serve the borscht-puree immediately.