Simmer chicken bones, vegetables, and herbs in 2.25 litres of water for 2 hours, skimming surface occasionally.
Strain the stock through a sieve and simmer further to concentrate flavor if needed.
Poach four eggs in simmering water for 3-4 minutes then cool in cold water.
Heat 1.5 litres of stock with salt and poach the chicken breast for 20 minutes.
Remove chicken to cool and boil the stock to cook the orzo for 8 minutes.
Slice the cooled chicken breast into thin strips.
Whisk remaining four eggs with lemon juice and temper with half the hot stock while whisking.
Return mixture to the pan and stir until thickened reaching 70–80°C without boiling.
Remove from heat and whisk in butter and chopped parsley.
Ladle soup into bowls, add chicken strips, a reheated poached egg, and a pinch of cayenne.