Cooking the onion.
Put the onions, butter, sugar, lemon juice and a little water in a saucepan and cover with cooking paper. Cook until the water has evaporated and the preparation is a little syrupy (reserve). 
Cooking the mushrooms.
Cut the mushrooms in 4 and sauté them with a little butter, salt and pepper (set aside).
Step 1: The chicken and the vegetables.
Cut the chicken in pieces, add salt and pepper and brown them with a little olive oil.
Step 2: Cover with stock, add the garnish and bring to a boil (skim if necessary).
Step 3:  Lower the heat, add the studded onion, the leek, the celery, the carrots, once the chicken and the vegetables are cooked reserve and keep the broth warm.
Step 4: Make the roux by melting the butter, then add the flour, cook lightly and moisten with 50 cl of hot broth, without stopping to mix until you get a smooth sauce.
Step 5: Add in the sauce the chicken, the vegetables, the glazed onions and the mushrooms, prolong the cooking so that the preparation is hot and not boiling.
Step 6: Add the link cream and egg prolong the cooking slightly without making boil.
Rectify the seasoning. Serve hot. Decorate with parsley and chervil.