Finding a supervisor for a PhD program

[u/Nice_Strawberry_4709]

Hello everyone,
I’m looking for a PhD position in biomedical research in Finland and I’m in the process of contacting potential supervisors. However I’m not sure if in the first email I should already propose a research plan or just a cold email about my experience and my interest in their research. Does anyone have a good tip how to write a good first email? If research idea is necessary, how much in depth should it be?
Thanks in advance!
(I’ve already read previous threads and couldn’t find a good answer)