This is apparently one of Jason’s trademark pieces, he just seems to like the shape apparently. One tip Jason had for all boxes was start with the top at the tailstock end. For the Pagoda boxes Jason works to a 1/5 to 4/5 ratio for top to bottom rather than the more usual for boxes of 1/3to 2/3.
Produce a chucking point on each end and the cut the lid section off. Put lid into chuck and drill a hole to mark the depth required and then hollow out curved interior. Only once as much wood has been removed as possible smooth the underside wings of the lid, this makes getting it flat easier. Cut the recess to fit the lid to the base. Next make the lip on the base to fit the top using the slight taper method (see inlaid lid for full explanation).
Create the rough outline of the base and refit lid using a personally produced liquid to help seal the lid to the base (spit). Shape the lid and create the finial. Remove lid. Drill hole to mark depth and hollow out base. Finish shaping outer surface and then square off end. Turn the box round and fit to a jam chuck. Jason explained he had tried many ways of holding such pieces but in the end a jam chuck works best for him. Undercut the base with a small curved hollow and then recess cut a basic circle around that to create a foot for the box (top). To finish square edges fit lid and then rub base and lid together over a flat surface abrasive moving the pieces laterally (not with the grain) in order to avoid damaging the corners. Jason the used a polishing mop held in the chuck to finish the surfaces all over.