I gave the girl a big doll, exactly what she longed to have.

what she longed to have 为名词性关系分句，what = the thing which。

= I gave the girl a big doll, exactly the thing which she longed to have.

你可以看出，what引导的名词性从句本质上是一个名词短语，被一个限制性定语从句所修饰。真正做 a big doll的同位语的，是what 所隐含的那个先行词 the thing.

所以，这种what从句要把它视为一个名词词组。