The incidents took place while he worked at Queen Elizabeth Hospital in Birmingham, where he was a liver, spleen and pancreatic surgeon for 12 years.
Liver surgeons use argon beam coagulators to stop livers bleeding during operations, but they can also be used to highlight the area of the organ due to be worked on.
It is not harmful and the marks usually disappear by themselves, but when the female patient had a follow up operation doctors saw they had not healed and saw the initials there instead.
Judge Paul Farrer allowed Bramhall to stand in front of the dock, in the well of the court, as the surgeon pleaded guilty to assaulting a patient whose name is protected by a court order during an operation in August 2013.
He also entered a guilty plea relating to an operation performed on an unknown patient in February of the same year.
Addressing the court after the pleas, Mr Badenoch said: 'This has been a highly unusual and complex case, both within the expert medical testimony served by both sides and in law.
'It is factually, so far as we have been able to establish, without legal precedent in criminal law.'
The barrister added that Bramhall was employed as a consultant surgeon in Birmingham at the time of the transplant operations and that both patients had been under anaesthetic.
'The pleas of guilty now entered represent an acceptance that that which he did was not just ethically wrong but criminally wrong,' Mr Badenoch told the court.
'They reflect the fact that Dr Bramhall's initialling on a patient's liver was not an isolated incident but rather a repeated act on two occasions, requiring some skill and concentration. It was done in the presence of colleagues.'
Describing the offences as an abuse of position, Mr Badenoch said they had been carried out with a disregard for the feelings of unconscious patients.
The prosecutor said of the assaults: 'It was an intentional application of unlawful force to a patient whilst anaesthetised.
'His acts in marking the livers of those patients were deliberate and conscious acts.
'Suffice to say, for current purposes, these pleas meet the broad public interest.
'It will be for others to decide whether and to what extent his fitness to practise is impaired.'
The offence of assault by beating was brought against Bramhall to reflect the act of marking the liver and there is no suggestion that he was responsible for physically 'beating' either patient.
Adjourning the case for a pre-sentence report, Judge Farrer told Bramhall: 'For reasons that you are aware of, I am not going to sentence you today.
'The prosecution need to do further work. Your legal team need to do further work in terms of completing the documents that you wish to place before me in due course.'
Bramhall, of Redditch, Worcestershire, was accused of causing actual bodily harm against a female patient on February 9 2013 and a male patient four months later on August 21.
He was suspended by the University Hospitals Birmingham NHS Foundation Trust after the allegations came to light.
A spokesman for the trust told MailOnline he no longer works there.
He resigned in 2014, with the trust commenting at the time: 'During the course of an internal disciplinary investigation into the conduct of Mr Simon Bramhall, the consultant liver surgeon has tendered his resignation which has been accepted by the trust.'
While he worked there he was also involved in tutoring and examining medical students and supervising postgraduate students.
