Roughly chop the soup greens and onion, leaving the onion skin on. Slice the spring onions. Brush the mushrooms clean and quarter them.
Heat vegetable fat in a saucepan over medium-high heat. Add the chicken breast with carcass and sear until browned on all sides, about 5-7 minutes.
Add the chopped soup vegetables and onion to the pan. Sear for 2-3 minutes without browning.
Deglaze with half the wine (Riesling or Silvaner) and let boil down for 3-5 minutes. Deglaze again with the remaining wine and let boil down for another 3-5 minutes.
Cover everything with water and bring to a boil, keeping the pot covered.
Carefully remove the whole chicken breast with carcass and set aside to cool. Reduce heat to low and let the broth simmer gently for 1 hour and 30 minutes with the pot covered.
When cool enough to handle, peel the skin from the chicken breast and remove the fillets from the bone. Set the fillets aside. Return the carcass to the simmering broth.
After simmering the broth for 1 hour and 30 minutes, strain it through a sieve and discard the solids (carcass and vegetables).
Degrease the broth by refrigerating for at least 8 hours and lifting off the solid fat layer, or use a fat separator jug to remove the fat.
Heat vegetable fat in a saucepan over medium-high heat. Sear the quartered mushrooms for 3-5 minutes. Add the sliced spring onions and sauté for 1-2 minutes without browning. Season with lemon juice, salt, and pepper. Set aside.
Pour the defatted broth into a sauté pan over medium-high heat. Add the sherry and let boil down for 3-5 minutes.
Add the cream and let boil down for 2-3 minutes. Repeat this process 2-3 more times (about 8-10 minutes of building time total) to gradually build the sauce.
Reduce heat to low. Gradually stir in the cold butter cubes until fully incorporated. Do not allow the sauce to boil. Season with salt, pepper, and freshly ground chilli.
Cut the chicken fillets into strips. Fold the chicken and mushroom mixture into the sauce over low heat. Warm gently for 2-3 minutes.
Serve with rice or potatoes and a glass of the Riesling or Silvaner wine used in cooking.
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