Shred beet and carrots and set aside while you melt butter over medium heat in a large pan. Dice and sauté onion until soft and translucent, but not browned. Add shredded beet and carrots and stir in ketchup and salt.
Cook for about 7-10 minutes, stirring frequently, until a strong, fragrant aroma arises. Remove from heat.
In a separate pot, bring chicken stock to a gentle boil. Add shredded cabbage and cook 2-3 minutes until the cabbage just starts to soften.
Add potatoes and cook an additional 4-5 minutes until fork tender. To this pot, add the carrot and beet mixture and return to a simmer for no longer than 1 minute to draw out the deep red color.
Remove from heat, add lemon juice, and taste, adding sugar or honey to lessen acidity until you reach a slightly sweet/savory flavor. To draw out full flavor and color, refrigerate soup overnight before serving. Garnish with fresh dill and sour cream.
