Dice one of the carrots. Place in a small saucepan with 1/2 cup chicken or vegetable broth; bring to a boil, turn on low and simmer for 10 minutes. Drain, saving the stock. Set cooked carrots and broth aside.
Dice remaining carrot and yams or place in food processor to coarsely chop. Combine the vegetables with the kasha, the reserved stock and remaining stock in a large saucepan. Bring to a boil, reduce heat and partially cover. Simmer until the vegetables are tender, approximately 30 minutes.
Strain the soup into a large bowl and puree the vegetables in a food processor or blender, in workable batches.
Combine the pureed vegetables and the soup again in the saucepan and heat well. Add the cayenne, nutmeg, and salt and pepper.
Put the reserved carrots in individual bowls, pour the soup over and add a dollop of yogurt in the center. Serve immediately. Makes 8 servings.