Well after almost a year of trying soaps made via a cold saponification process and switching back to the soap made with the hot saponification process I say that the soap made with the cold saponification process is the best there is.
The skin is a lot less dry, it's more elastic and for some reason I don't understand it protects against fungi.
I'm going to try and sell the hot processed soap that I have and buy cold processed soap, it's of good quality but I have too much issues with my skin nowadays.

@mangeurdenuage any recommendations? sounds interesting!

@bonifartius
My two favorites:
https://savonneriedescevennes.com/savons-au-lait-d-anesse-bio/49-savon-a-froid-au-lait-de-d-anesse-biologique.html
or
https://savonneriedescevennes.com/aux-huiles-essentielles-naturelles/25-savon-a-froid-a-l-huile-essentielle-bergamote-gingembre.html

@mangeurdenuage thanks! i currently have a plain olive oil soap which is made using the hot process, but this sounds nice. it's the only soap i use anyway, even for the head, so it's probably good to have something a bit less aggressive :)

@bonifartius
>plain olive oil soap
They have some and it's the one I'm currently using. The difference is that there's also some donkey milk.
https://savonneriedescevennes.com/savons-au-lait-d-anesse-bio/55-lait-d-anesse-bio-olive.html

@mangeurdenuage it's not really about the olive oil but about not having so much shit in it. Soap from the supermarket always is full of other stuff, so i got one from the net which is just soap (and a bit of green dye because people seem to expect that). i'm happy with it in general, but the cold saponification is interesting. donkeys milk sounds a bit like if made for cleopatra :D