Mix flour and margarine together in a saucepan over medium heat, stirring until the flour and margarine form a paste.
Whisk cream into flour mixture about 1/2 cup at a time until smoothly combined; whisk in chicken broth and parsley. Bring sauce to a simmer, whisking constantly until thickened.
Whisk egg yolks and lemon juice together in a bowl.
Whisk egg yolk mixture slowly into cream mixture, about 1 tablespoon at a time, until the sauce barely comes to a simmer and coats the back of a spoon. Do not boil.
If thicker sauce is desired, whisk cornstarch and 1/4 cup of sauce in a small bowl; stir cornstarch mixture back into sauce until thickened, about 2 minutes.
Stir chicken breast pieces into sauce until chicken is heated through.
