Quill of Correspondence
Sold by Lady Ilinca. Not sure why there's a salty person out there downvoting the letter contents, but as someone else mentioned, there may turn out to be interesting lore in these letters.
The Quill of Correspondence is a Shadowlands toy sold by Lady Ilinca in Revendreth that lets you channel a letter-writing animation, after which you receive a reply in your mailbox from a Shadowlands character within a day.
Guide awaiting review
Find Lady Ilinca
Travel to Revendreth and find Lady Ilinca at 28.4, 41.0 to browse her vendor inventory.
Purchase the Toy
Buy the Quill of Correspondence from Lady Ilinca. No price was listed for this item.
Tips
The toy appears to write to whichever contact you currently have as your Best Friend through the Covenant system, and there is no option to choose which character receives your letter.