Bring the chicken broth and chicken breast to a boil. Cover and simmer for 10 minutes. Turn off the heat and allow the chicken to sit in the stock for another 10 minutes.
Take the chicken out of the broth and wrap in aluminum foil to keep warm.
Bring the chicken broth back to a boil and reduce the broth by half. Add the cream and garlic and bring back to a boil. Simmer for 5 minutes.
Beat the egg yolk in a boil, add some of the broth/cream mixture and mix thoroughly. Add more broth until yolk/broth mixture is warm, mix thoroughly.
Add yolk mixture to remaining broth/cream mixture and warm the egg.
Add cheese and parsley and season with salt and pepper.
Cook pasta according to directions on packaging and drain.