The Birthday Toast was an event held each year at a small gathering in honour of both Bilbo Baggins' and Frodo Baggins' birthdays, held each year on the 23rd September at Bag End (both hobbits shared the same birthday).
This custom began after Bilbo left Bag End after the celebration of his 111th birthday - A Long-expected Party.
Tolkien Society tradition
The Tolkien Society has upheld this tradition through a Birthday Toast in honour of the creator of Bilbo and Frodo - J.R.R. Tolkien and is held on the author's birthday, 3rd January, each year. The 'toast' itself is: "The Professor".