Place the chicken cubes, carrots, onion, and bouquet garni in a large pot and cover with chicken stock and white wine.
Bring to a simmer over medium heat, then reduce heat to low and poach for 20-25 minutes until chicken is cooked through.
While poaching, sauté the mushrooms in a separate pan with 10g of butter until tender and set aside.
Drain the chicken and carrots, reserving the cooking liquid (stock); discard the onion and bouquet garni.
In a clean saucepan, melt the remaining 30g of butter and stir in the flour to create a roux; cook for 2 minutes without browning.
Gradually whisk the reserved poaching liquid into the roux and simmer until thickened into a smooth velouté.
In a small bowl, whisk together the heavy cream and egg yolks to create a liaison.
Temper the liaison by adding a ladle of hot sauce to the cream mixture, then slowly whisk the mixture back into the main saucepan over low heat; do not boil.
Fold the chicken, carrots, and mushrooms back into the sauce.
Add lemon juice, salt, and white pepper; garnish with fresh parsley and serve immediately.