How to frame self-study in an SoP

I am eager to pursue a PhD after completing my Master's degree. Although there is limited overlap between my current studies and the field I want to focus on for my PhD, I am passionate about this area and have been dedicating myself to self-study alongside my Master's program.

I had a conversation with an administrator at my Alma Mater, Berkeley, who mentioned that this approach is possible. However, I wanted to reach out and learn if others have had similar experiences, and if anyone has advice on how to present this in my Statement of Purpose, especially given that I don’t yet have a degree or official transcript with letter grades in the field I'm targeting. Any insights would be greatly appreciated!

Thank you!