I am a permanent resident of California but I spend more than 336 days abroad. I want to begin working remotely for a Hong Kong based company. How do I file taxes?

Residents of California are taxed on ALL income, including income from sources outside California.

See page 6 of this reference:  https://www.ftb.ca.gov/forms/2019/2019-1031-publication.pdf

Your possible tax obligations to Hong Kong are beyond the scope of this forum.