Bring 2 liters of water to a boil over high heat. Add the chicken, cover, reduce heat to medium, and cook for 45 minutes.
Roughly chop the soup greens, garlic, and onion. Add them to the pot along with a piece of lemon peel, bay leaf, white peppercorns, fresh thyme sprig, and one bunch of parsley. Season with salt, cover, and cook over medium heat for 45 minutes until the chicken is tender.
Remove the chicken from the pot and cut into bite-sized pieces.
Skim fat from the broth surface if desired. Measure out roughly 1 liter of broth.
Melt 60 g butter over medium heat. Stir in 50 g flour to create a smooth paste.
Gradually add the broth while stirring constantly to avoid lumps. Add the peas, roughly chopped asparagus, juice from the lemon, and grated lemon zest. Simmer over medium heat for 10 minutes.
Whisk 1 egg yolk with 200 ml cream in a small bowl. Stir this mixture into the sauce. Season with salt and pepper to taste. Stir in the remaining parsley and chives, finely chopped.