In Lathe of Heaven by Le Guin, the main character George is famously frustrating because he doesn't do much. Bad things happen to him and he basically just lets them. He thinks his psychiatrist is totally evil yet keeps going back. He has a pitiful lack of control over his life. He doesn't seem to want control, which is the worst part. He isn't super happy, and you could take that as the main point, but I don't.
even George, perhaps the most boring and least reactive person you've ever read about or met, would just laugh at the goal of being "entirely unfazed by everything happening around you." Even he falls in love, experiences great joy and brutal heartbreak, finds his own small ways of making an impact, makes peace with difficult things. For a character who supposedly does nothing important, he does a hell of a lot.
even George, perhaps the most boring and least reactive person you've ever read about or met, would just laugh at the goal of being "entirely unfazed by everything happening around you." Even he falls in love, experiences great joy and brutal heartbreak, finds his own small ways of making an impact, makes peace with difficult things. For a character who supposedly does nothing important, he does a hell of a lot.
Good luck, I guess!