What's your best idea for a remote team event?

With organizations moving to remote, either temporarily or permanently, many of the co-located team events we used to love no longer work very well. Small, self-forming conversations within a larger group (like a mixer or cocktail party) just don't translate to online, and even general group talks promote a widening divide between those who aren't confident interjecting and those who dominate the conversation.

There are some activities that benefit from being remote and spread across geographies; anything that's naturally asynchronous or involves a component of individual concentration can be better than the in-person variation. One example, instead of a traditional hackathon I had great success with a daily coding challenge we ran for a month. None of the problems were too challenging (with a focus on broad participation), we had a funny (but ridiculous) story-based theme and gave out lots of fantastic prizes (during the entire event, both random and performance-based).

I need more great ideas! What's your tip or suggestion for an activity or event that really promotes team cohesiveness and relationship building when you can't physically be together?