Trim and cut the Veal Shoulder into large, even cubes; pat dry and season lightly with Salt.
Place the meat in a large stockpot with a halved Onion studded with Cloves, sliced Carrots, roughly chopped Leek and Celery, a Bouquet Garni, and cold Water to just cover the ingredients.
Bring to a gentle simmer over medium-low heat, skim off any foam that rises, cover partially and cook gently for 1½–2 hours until the veal is very tender.
While the veal simmers, peel the Pearl Onions (briefly blanching makes peeling easier) and wipe or slice the Button Mushrooms. In a skillet, sauté the pearl onions and mushrooms in Butter over medium heat; add a pinch of Sugar, a little Salt and a squeeze of Lemon Juice to glaze and lightly brown them, then remove from the pan and keep warm.
When the meat is tender, lift the veal and the large cooked vegetables from the pot, reserve the solids, and strain the cooking liquid through a fine sieve; reduce the strained stock by simmering if you want a more concentrated flavor.
To make the sauce, melt a knob of butter in a saucepan and stir in the Plain Flour to form a pale roux; cook briefly, then whisk in the hot strained stock a little at a time until smooth and simmer until it thickens into a velouté.
Off the heat, whisk together the Crème Fraîche and the Egg Yolks with a bit more Lemon Juice; temper this mixture by whisking in a ladle of the hot sauce, then slowly blend it back into the pan. Warm gently—do not boil—or the eggs will curdle.
Return the veal, the sautéed mushrooms and glazed pearl onions, and the cooked carrots to the sauce and heat through gently so everything is evenly coated.
Adjust seasoning with freshly ground White Pepper and additional Salt to taste, finish with a handful of chopped Flat-Leaf Parsley and a final pat of butter for gloss, then serve immediately with rice, mashed potatoes, or buttered noodles.
