([![]]+[][[]])[+!+[]+[+[]]] has two parts :
([![]]+[][[]]) and the other which you found yourself.
![] returns false. Then we use [...] to get the .toString() behavior of +.
([]+[] is the same as [].toString()+[].toString())
the [][[]] is undefined because we're trying to access the index [] (or [].toString(), which is '') of [] which is undefined.
Sorry for the previous answered, I misread your comment totally.
