In short, when it's important to switch to writing to have the time to choose your words or even translate your ideas from another language to English. When you have to have live conversations, make them face-to-face instead of via a remote call and use drawings to show what you say.
Move to long text and asynchronous conversations when important
One aspect that helps a little bit, especially when it's hard to understand each other and you need to be precise, is to switch from live conversation to asynchronous conversation over long-form text like email.
This allows people to write down their thoughts in their own language and then use a tool to translate it.
Then you can answer in English, and the other person can translate it back.
Making it asynchronous removes the pressure of finding the words on the spot and also eliminates the issue of not getting the accents of one another.
Use face-to-face and drawing when it has to be live
When the interaction has to be live, I try to push for two things:
Live: Make it in real life instead of over a video call (it's easier to understand accents when you are in front of each other, and body language helps a lot).
Drawing: Use drawing to summarise the conversation and show visually what you're talking. It also helps when asking questions to draw the different options :)
That's my take working with many non-native English speakers within the Master Service Design of the Lucerne University of Applied Sciences and Arts and being a non native English speaker myself :)
Thanks to Daisy Wu who inspired this post by sharing a question and great meme on Linkedin