In a large saucepan placed over a medium heat, combine the tapioca, the 2-½ cups of coconut milk, and the vanilla bean.
Bring to a simmer over a moderate heat and cook, whisking occasionally, until the tapioca is translucent and tender (about 20 minutes). Whisk in the remaining coconut milk.
In a small bowl, whisk the egg yolks with maple syrup (if using) until smooth. Pour in about ½ cup of the hot coconut very slowly while continuing to whisk the entire time. Make sure to take your time with this step, otherwise you'll end up with scrambled eggs!
Then pour the egg/coconut mixture back into the saucepan, stirring constantly, and keep stirring for about 5 minutes.
Refrigerate the pudding until solid, and serve chilled.