This is partly just for my reference, but I get a fair number of hits from people looking for borscht recipes, so I thought I'd post it here. I went over to my friend Aina's the other day and found her making borscht for her brothers. "If it's borscht, shouldn't it have beets in it?" I asked. "It can, but it doesn't have to," she replied. To Aina and to many Russians, borscht means 'cabbage soup,' not necessarily 'beet soup', as Americans tend to think.
This is all quite approximate. Russians aren't nearly as recipe-obsessed as Americans are; for example, I remember one of my classes laughing out loud at the fact that our recipes tell us to preheat our ovens, and my Russian girl friends often have to hide their skepticism of my ability to cook, since I appear to require instructions that are, to them, far too specific. Anyway, for soup, amounts don't really matter as long as you don't oversalt it.
Start by peeling and slicing three or four potatoes (Aina cuts them in half lengthwise, and then slices each half widthwise into centimeter-thick slices) and shredding a whole head of cabbage. Take a tablespoon or so of dried mint (she does this for her Turkmen father; mint is apparently prominent in Turkmen cuisine) and use your hands to mix it and some salt to taste into the shredded cabbage.
Put the cabbage and potatoes to boil in a 5-liter pot with broth for at least 15 minutes. Aina used meat broth, but no meat. I'm pretty sure any kind of broth would do. I didn't see how much she had in there, but it was enough so that the broth and the cabbage mixture combined almost filled the pot.
Meanwhile, grate a carrot with the large holes of a grater and chop an onion; put them in a pan with some vegetable oil over medium-low heat and get to work chopping three or four tomatoes. Add those to the pan, along with a spoonful of tomato paste for color; bring the pan contents (now quite liquid because of the tomatoes) to a boil while chopping some garlic to taste. Add everything to the soup pot. Now chop some fresh parsley and dill (maybe about half a cup chopped) and add that, along with some more salt. Let everything simmer for a minute or two more, and your borscht is done. Serve with a dollop of sour cream or mayonnaise in each bowl.
P.S. It seemed weird to me that Russians eat soup in the summer, but with some bread and a salad of chopped tomatoes/cucumbers/parsley/dill (ubiquitous in Russia from May to October) it made a nice, fairly light dinner. And it's quick, if you've got the broth on hand already.