Keeping roots and stems intact, rinse beets thoroughly under running water; set aside.
In Dutch oven or large saucepan, melt half of the butter over medium heat; cook onions until softened and translucent. Add tomatoes, breaking up with fork. Add stock, beets, 4 of the potatoes and caraway seeds; bring to boil. Reduce heat, cover and simmer until potatoes are tender, about 30 minutes. Remove potatoes to bowl; mash until smooth and set aside. Cook for 15 to 20 minutes longer or until beets are cooked through. Remove beets and place under cold running water; slip off skins. Grate into bowl and set aside.
Return mashed potatoes to pan, stirring until blended. Cut remaining potato into large dice; add to pan along with carrots, rutabaga, grated beets and 1 tsp (5 mL) salt. Cover and simmer gently until diced vegetables are cooked through, 8 to 10 minutes.
Meanwhile, melt remaining butter in large skillet. Add green cabbage and cook until color brightens; stir into soup and cook, uncovered, for 3 minutes. Add red cabbage and dillweed to soup; cook for 3 minutes or just until cabbage is tender-crisp. Add more salt and pepper to taste if desired. Ladle into warmed soup bowls and dollop with yogurt.
*Note: To make thick, creamy-tasting yogurt topping for borscht, place Balkan-style yogurt in a cheesecloth-lined sieve set over bowl. Refrigerate and let drain for 1 hour.
