belvedere
/ˈbɛlvəˌdɪr/
noun
A summerhouse or open-sided gallery, usually at rooftop level, commanding a fine view.
Here NGP proposes inserting what is effectively a completely new glazed building into the hole, rising on tall columns to provide an inhabited roof level with a cyclopean belvedere of a west wall.
arbour,shady place,leafy shelter,alcove,recess,pergola,grotto,sanctuary