It's a taste from my childhood, too. From Raymond Skolov's The Jewish American Kitchen (1989):

Cabbage and Meat Borscht

1 or 2 marrow or knuckle bones
3 lbs flanken
2 cups chopped onions
2 garlic gloves, peeled and crushed
1 green cabbage (2 ½-3 lbs), cored and shredded (about 12 cups)
1 tbsp caraway seeds
2 tsp salt
Freshly ground black pepper
3 tbsp lemon juice
1 tbsp sugar

In a 5 or 6-quart soup pot, cover bones and flanken with 3 quarts of water. Bring to a boil. Lower the heat and simmer for 15-20 minutes. Skim any foam as it rises to the surface.
Add the onions, garlic, cabbage, caraway seeds, salt, and pepper. Stir to combine. Cover the pot and simmer for 2 hours.
Remove the flanken and marrow bones and continue simmering the soup. Slice the meat off the bones, discarding fat and gristle. Put the sliced meat back in the pot. Add lemon juice and sugar, and simmer for 30 minutes. If serving immediately, skim any fat.
If waiting, strain the soup and refrigerate the liquid and solids separately. After 8 hours, the fat will harden and can be removed easily. Recombine the broth and solids and bring to a simmer before serving. Season with additional salt, lemon juice, and/or sugar, to taste.
Makes 8-10 servings.

Here's one that includes a couple of variations. I add a handful of raisins in the broth to add the occasional sweet bite and add a little splash of vinegar at the end for that slighty sour/pungent note. http://www.suite101.com/content/cabbage-borscht---german-russian-cabbage-soup-a207625

You could try this one: http://www.homemade-chinese-soups.com/borscht-soup.html The Chinese have this version, and we call it "Russian" soup... which is perfectly non-descript and inaccurate... but hey, if it works...