Preheat the oven (with one of its racks positioned in the center) to 400ºF. Line a large rimmed baking sheet with foil and add the chicken bones. Transfer to the oven and roast until the bones are a dark golden brown, about 1 hour.
To a large pot set over medium-high heat, add the roasted bones, the whole chicken, and enough cool water to cover the chicken by 3 inches. Bring to a boil, skimming off and discarding any froth that forms along the surface then lower the heat to maintain a simmer and add the onions, parsnips, carrots, fennel, celery, parsley, kombu, bay leaves, and salt, then continue cooking until the broth turns a deep golden color, at least 4 and up to 6 hours.
Set a fine mesh sieve over another large pot. Using tongs, transfer the chicken to a large bowl and set aside to cool slightly. Strain the broth into the second pot, reserving the parsnips, carrots, fennel, and celery and discarding all the other solids. Transfer the vegetables to an airtight container and once cool, transfer to the fridge. Separate, and reserve the chicken meat, discarding the skin and bones. Transfer to an airtight container and transfer to the fridge.
Allow the broth to cool to room temperature, then transfer to the refrigerator to chill until the fat solidifies on the surface, 2–3 hours or overnight. When the broth has chilled, skim off the chicken fat and reserve it for the matzo balls. (If you have less than ¼ cup of fat, supplement it with store-bought schmaltz or olive or canola oil.)
In a large bowl, stir together the eggs, matzo meal, reserved chicken fat, stock, cilantro, parsley, salt, black pepper, and ginger. Cover and refrigerate until chilled, at least 1 and up to 24 hours.
Fill a wide, deep pot halfway with lightly salted water; bring to a boil over medium-high heat. With wet hands, gently divide and shape the matzo mixture into eight 3-tablespoon portions and roll into balls, gently dropping them into the boiling water as you go. (Do not pack the dough tightly or the balls will not puff as they cook.) Lower the heat to a simmer, cover the pan with a lid, and cook until the matzo balls expand, float to the surface, and are evenly cooked through, about 25 minutes. To test if they’re ready, remove one matzo ball with a spoon and cut it in half; it should be the same color throughout and have a consistent light texture.
Meanwhile, return the stock to the stove and set over medium-low heat. Shred the reserved chicken into bite-sized pieces and add it to the pot. Coarsely chop the parsnip, celery and carrots, and add them back to the pot as well. Cook until heated through, 7–8 minutes, then season to taste with more salt and black pepper. Divide the soup among 4 wide soup bowls. Use a slotted spoon to add 1–2 matzo balls to each bowl, then top with chopped parsley, and serve hot.