For the bouquet garni, combine all the ingredients together in a cheesecloth. Tie it up and set aside.
Place the meat in a large pot and cover with cold water. Bring to a boil and blanch for 3 minutes; skim off any foam on top. Drain the meat, rinse quickly under cold water and transfer the cubes to a Dutch oven.
Stud the white onion with cloves and add it to the meat along with carrots, celery and the bouquet garni. Cover with chicken broth and season with white pepper. Bring to a boil, reduce the heat to medium low and simmer gently for 1 ½ hours or until the meat is tender.
Meanwhile, in a medium saucepan on medium heat, add butter, bacon fat and lemon juice. When it starts simmering, add white wine and mushrooms. Stir to coat the mushrooms, cover and simmer for 5 minutes. Transfer the mushrooms to a bowl using a slotted spoon, and pour the remaining liquid into the Dutch oven; stir.
In a small pot with boiling water, add the pearl onions with skin on and boil for 3 minutes. Drain them in a colander and rinse under cold water. When cool enough to handle, peel off the skin and set aside.
In a small saucepan over medium heat, add butter and sugar (glacé à blanc). Stir, add the peeled onions and pour in enough cold water to cover them; add a small pinch of salt. When it starts simmering, cover, reduce the heat to medium low and cook for 20 minutes or until the tip of a sharp knife goes in easily. Transfer the pearl onions to a bowl and set aside; discard the liquid.
When the veal is cooked, remove the onion, bouquet garni and celery; discard them. Set the carrots aside and transfer the meat to a bowl. Strain the broth through a fine sieve over a large bowl; discard any solids. The amount of the broth needed for the recipe is 4 cups. If there’s not enough, top up with some water.
Wash the Dutch oven and return it to the stove over medium heat; add butter. When melted, add flour and whisk until the flour is cooked, about 1 ½ minutes.
Whisking constantly, pour in 2 cups of the reserved broth. Add the remaining broth, heavy cream and lemon juice. Whisk until the sauce has reduced by half. Taste and adjust seasoning before adding the meat, mushrooms and pearl onions. Stir to combine and cook until the ingredients are heated through.
The blanquette can be served as is or add the carrots. If the vegetable is added, cut it into the same size pieces as the veal. Heat the carrots through for 1 minute before pouring in the cornstarch mixture; stir until the sauce thickens, about 45 seconds.
Before serving it over rice or noodles, garnish with finely chopped parsley.