Place the beet pieces into a one-quart mason jar. Fill the jar to within one inch of the neck with filtered water.
Add the whey or sauerkraut juice.
Cover, screwing the lid on loosely to allow gasses to escape. Or, preferably, use Airlock Lids (find link in Recipe Notes).
Keep the brew at warm room temperature and out of direct sunlight for two days in warm weather, or up to 8 days or longer in colder weather. In cold weather, I recommend using a warming mat or yogurt maker for a warm steady temperature, to prevent spoilage or kahm yeast from developing.
After the kvass has deepened in color, has a pleasantly sour flavor, and shows signs of bubbles near the surface, or active effervescence, strain it into a fresh jar, and reserve beets. (Also reserve about 1/4 cup kvass in the original jar if you want to make another batch!) Add the raspberries and optional sweetener to fresh jar of kvass. Stir to dissolve sweetener.
Transfer to the refrigerator. Chill and serve within one week. (Strain out the raspberries when serving, if desired, or add fresh ones for garnish.)
To make another batch: Have beet chunks and 1/4 cup kvass in original jar. Fill this jar again with fresh filtered water or cooled hibiscus tea. (Do not add new whey.)
Again, keep the mixture at warm room temperature for 2 to 8 days.
This second beverage may be milder and less potent than the first, (which is when and why I like to substitute the healthful hibiscus tea for the water). The beets are now “exhausted” and can be thrown away, but ¼ cup of the strained kvass may again (!) be used for a following batch in place of whey.
Recipe Variations: The above listed optional additional ingredients can be fermented with the beets for added flavor variations and nutrition, then strained out with the beets.