Log in to your Twitch account
Click your profile icon
Open Creator Dashboard
Go to Settings
Select Stream
Turn on Store past broadcasts
Stream a live broadcast
Go to Video Producer
Find the VOD you want to save
Click the three-dot menu next to the VOD
Select Download to save it locally
If needed, use Highlight to keep a shorter saved version on Twitch
If needed, use Export to upload the VOD to YouTube
Check your VOD retention settings to make sure broadcasts are saved long enough