Place the meat in a large pot. Cover with cold water. Bring to a boil and blanch for 3 to 4 minutes. Rinse under cold water. Drain.
Return the meat to the pot. Add the bouquet garni, carrots, celery, onion, garlic and broth. Lightly season with salt and pepper. Bring to a boil, reduce the heat and simmer gently for 1 hour, uncovered.
To easily peel the onions, blanch in boiling water for 2 to 3 minutes. Rinse under cold water and peel. In a saucepan, lightly brown the onions in butter. Also cook the mushrooms in butter until the water has evaporated or without butter in the microwave.
Pass the meat, vegetables and broth through a sieve. Set the meat and broth aside separately. If you don’t get a litre (4 cups) of cooking broth, add water.
In a clean pan, melt the butter. Add the flour and stir for 1 minute. Add the cooking broth. Whisk until it slightly thickens.
In a bowl, whisk together the cream and egg yolk. Add a ladle of the sauce to slowly warm the egg. Whisk this mixture into the sauce.
Add the meat, onions and mushrooms. Remove from the heat, adjust the seasoning. Serve with rice. A mixture of white and wild rice would be tasty.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.