In a medium bowl, combine the eggs, fat, and soda water and then add the matzo meal. Add the 2 teaspoons salt, a few cranks of black pepper, and the ground caraway. Stir all the ingredients together lightly with a spatula or a wooden spoon. Set aside in the refrigerator for 30 minutes. Bring a large pot of salted water to a boil over high heat. Form 1- to 2-inch balls of the mixture with your hands or a scoop. Do not compress or overwork the mixture or they will be tough. Decrease the heat to medium-high and drop the balls into the simmering water and cook for 25 minutes. Remove with a slotted spoon, drain, and set aside on a plate.
For the soup, add the vegetable oil to a sauce pot set over high heat. Decrease the heat to low and add the pearl onions, celery, carrots, and turnips, and cook for 2 to 3 minutes. Add the stock and season with salt and pepper. Bring to a boil and decrease the heat to a simmer. Add the matzo balls to the soup and simmer for 5 minutes, or until the vegetable are tender.
To serve, spoon a few matzo balls into soup bowls and divide the vegetables and soup between the bowls. Add a couple of the roasted beet halves to each bowl and sprinkle with the parsley. Serve immediately.