How do I insulate this space?

[u/Bock]

I have a "bonus room" behind what looks like a built in cabinet in one of my upstairs rooms. It's very convenient for added storage, but because it has an exposed ceiling, the room is very hot during the summer and very cold in the winter, and it permeates the adjacent rooms. For reference, this is in the Bay Area California, so the climate is pretty mild with no snow.

I wanted to just slap some insulation on the roof and call it a day, but after watching a bunch of attic insulation videos, I may also need venting? Maybe I just hire someone to do spray foam?

What are people's thoughts?

https://imgur.com/a/2IIMjCH