In a medium bowl, whisk together eggs and chicken fat until combined. Whisk in 1/2 cup water and salt. Add matzo meal, and whisk until combined. Cover and refrigerate batter until firm, 2 to 4 hours.
Line a baking pan with parchment. Bring chicken stock to a boil in a large wide saucepan, and reduce heat to a simmer.
Slightly dampen your fingertips, and form 2 heaping tablespoons of batter into a 1 1/2-inch ball, being careful not to compress the mixture too much. Place ball on the prepared pan. Repeat process with remaining batter.
Using a large spoon, slide the matzo balls into the simmering stock. Once all the balls have been added, cover and cook for 10 minutes. Add carrots and parsnips, cover, and continue cooking for 20 to 25 minutes, until the vegetables are tender and the matzo balls are cooked through. To test if the matzo balls are done, remove a ball from the water, and slice in half. The color should be light throughout. If the center is darker, cook 5 to 10 minutes more.
To serve, fill the soup bowls evenly with soup and vegetables, allotting each person one or two matzo balls, depending on his or her appetite. Garnish with fresh dill, and serve immediately.