Step 1

To make the “beet water,” roughly chop 2 pounds of the beets (select the smaller ones), preferably in a food processor fitted with the metal blade. Place the chopped beets in a large stockpot. Add 10 cups of water and 1 tablespoon vinegar.

Step 2

Place the stockpot over high heat and bring to a boil, then reduce the heat to low, and simmer for 2 hours. (If it seems like the liquid is evaporating too quickly, you may need to cover the pot partially with an offset lid.) The beets should be extremely soft and the liquid bright red.

Step 3

Strain the liquid, pressing the cooked beets against the side of the strainer to extract as much liquid as possible. Discard the pulp or reserve. Set aside the beet water. You should have just about 4 cups.

Step 4

Meanwhile, place the remaining 1 pound of whole beets in a separate large stockpot. Add water to cover and bring to a boil. Reduce the heat to low, and simmer until the beets are tender-firm, about 40 minutes. When the beets are cooked, add 1 tablespoon white vinegar and set them aside to cool.

Step 5

When the whole cooked beets are cool enough to handle, peel them; the skins should slip off easily. Grate the peeled beets on the largest holes of a box grater or in a food processor fitted with the grating blade.

Step 6

To make the broth, place the pork butt in a large stockpot and add the beef stock. If necessary, add a little more stock or water to cover. Add the bay leaf, allspice berries, and peppercorns. Bring to a boil, reduce the heat to low, and simmer until the meat is tender and beginning to fall apart, about 2 hours. Set the pork aside to cool. When the pork is cool enough to handle, remove it from the pot and cut the meat into ½-inch cubes. Strain the broth and discard the bay leaf, allspice berries, and peppercorns. Reserve the cubed meat and 4 cups of the broth.

Step 7

To cook the vegetables, place the carrots and celery in a large stockpot and pour the reserved meat broth over them. Bring to a boil, reduce the heat, and simmer until the carrots and celery are just tender, about 8 minutes. Add the cabbage and potatoes and continue to cook until the potatoes and carrots are easily pierced with a pairing knife but keep their shape, 15 to 20 additional minutes. Add the lima beans and cook for 5 additional minutes, just to meld the flavors. Gradually add the remaining 7 tablespoons white vinegar, tasting between additions and stopping when the flavor is to your liking. Remove the soup from the heat and set aside.

Step 8

To compose the soup, in a large soup pot combine the “beet water” and meat broth with the vegetables. Add the cubed pork and the grated beets. Stir to combine and bring to a simmer over low heat. Season to taste with salt and serve immediately.