OK -- I get that now. So I added:

where rn=1 (so it would be included)

and removed the top 1, so I now looks like:

select nco.*, nci.ORDER_ITEM_ID o2

From OR_NCCore.dbo.Order_Dim nco

INNER JOIN or_nccore.dbo.STATUS_DIM S

ON nco.STATUS_ID = S.STATUS_ID

cross apply (

select *,rn=row_number()

over (partition by order_id order by order_item_id asc)

from or_nccore.dbo.ORDER_ITEM_DIM nci

where nco.order_id=nci.order_id

) nci

where rn=1

The inner join still beats it by a wide margin on I/O, even after I added the index you suggested (thanks for that!) It's also a pity that I can't put the where clause inside the subquery for the cross apply, but such is life!