Prepare the ingredients. Trim the veal shoulder and cut into even ¾-inch (2 cm) pieces. Finely dice the onion; cut carrots, parsley root, and celery root into roughly ¼–⅓-inch (7–8 mm) dice. Mince the garlic. Peel the potatoes and cut into about ⅝-inch (1½ cm) pieces; hold in cold water until needed, then drain. Keep raw meat and egg handling separate from ready-to-eat ingredients.
Soften the vegetables. Melt the butter in a heavy soup pot over medium heat. Add onion, carrots, parsley root, and celery root. Cook, stirring regularly, for about 6 minutes, without deep browning.
Add the veal. Stir in the veal and garlic and cook for about 4–5 minutes, until the meat’s raw-looking surface changes color. Do not build a dark crust. This surface change does not mean the meat is fully cooked.
Cook the flour lightly. Sprinkle the flour evenly over the meat and vegetables and stir for about 1 minute. Keep it pale; do not brown it.
Add the water and seasoning. Gradually stir in a small part of the measured hot water until the flour is smoothly dispersed, then add the remainder. Add the bay leaf, the initial-seasoning salt, and black pepper.
Simmer gently. Bring slowly to a gentle simmer, skim any foam, and reduce the heat. Cook with the lid slightly ajar for about 45 minutes, stirring occasionally. Avoid a hard boil or excessive evaporation.
Cook the potatoes. Add the drained potatoes and simmer another 20–25 minutes, until the veal is tender and the potatoes are fully cooked. Remove the bay leaf. Pull the pot off the burner. Before adding the egg-and-cream mixture, let the base cool off heat to about 165–167°F (74–75°C), stirring and checking with a thermometer. The cooling time varies; keep the soup off direct heat during this adjustment.
Temper the liaison. Whisk the full-fat cultured sour cream and egg yolk smooth in a heatproof bowl. Slowly whisk in a small ladleful of hot soup, then add more in small portions while whisking continuously, until the mixture is warm and fluid. The Notes give approximate tempering-soup volumes for each batch size; this liquid comes from the pot, not additional water.
Incorporate the liaison. With the soup pot off direct heat, pour the tempered mixture back in gradually, stirring constantly. Do not pour the cold egg-and-cream mixture straight into boiling soup.
Heat under thermometer control. Return to very low heat only as needed. Stir and check several places until the completed egg-containing soup reaches 162–167°F (72–75°C), at least 160°F (71°C) throughout. If already in range, keep it off the heat. Do not let it boil vigorously; do not judge egg safety by steam or appearance alone.
Finish the seasoning. Stir in the separate finishing salt, measured lemon juice, and finely chopped flat-leaf parsley. The broth should be creamy and lightly coat a spoon while remaining fluid, with distinct meat and vegetable pieces.
Rest and serve. Remove from heat and let stand for about 5 minutes, then serve hot. Refrigerate leftovers promptly in shallow containers as described in the Notes; avoid leaving the full pot out to cool for hours.