Hi Ryder 19!
An interesting situation you find yourself in! I am a CFI of an approved training organisation however that doesn't have any formal meaning in modern aeronautical parlance. A CFI (and I'm talking UK here, the term has another meaning entirely in the USA) is usually an experienced and mature Flying Instructor, usually also qualified as an examiner, who is employed as CFI by a training organisation.
The position of CFI has no formal definition within current EASA aeronautical management structures but the term is still used colloquially. Under EASA regulations the person who has formal responsibility for the delivery of training at an Approved Training Organisation is called the "Head of Training" or HoT. In my organisation I am the HoT but we still use the informal title CFI
It is possible for there to be a CFI who is not HoT, for example, a large training school might have a HoT who holds the formal and legal responsibility but working under him there could well be a CFI single engine, CFI Multi engine, CGI (Ground Instructor) etc.
I frequently perform a "functional hearing test" for a number of pilots who formally fail their medical hearing assessment but are then referred by the Medial branch to me as CFI for this assessment. It requires that I fly with them and make a practical assessment to determine if their hearing causes any functional impairment of their duties in the air. Based on my assessment the CAA then issues a normal medical.
So, picking the bones out of all this I surmise that the Medical branch are asking for you to get a functional assessment of your ability to speak clearly and to be understood while performing as member of a flight crew. If your stammer is slight (and as you say they wouldn't have known had you not mentioned it, it must be!) then I doubt it will be a problem.
Speak to the medial branch but I'd suggest that you plan to start your flying training (you don't need a medical to fly the dual training flights) at an Approved Training Organisation of your choice. Speak with the HoT at the ATO before you start and explain the situation to him. I'd anticipate that he will have a conversation with you and consider whether your stammer is likely to cause difficulty during training, assuming not he can start the training and after a few flights he can write to the medics stating that your slight stammer has no adverse affect on your ability to perform as a pilot. They will then issue the medical. Maybe they have a form he needs to complete? Ask them!
I have known and flown with several pilots who have stammers, in one case it's quite severe so I hope this will not be a show stopper for you.
Good luck!
3 Point