The Papa Stour Stofa is believed to have been used as a meeting place for representatives of the Norwegian King to conduct business on his behalf on the island. It is from this site that Shetland's oldest document originates. This document was a record of a quarrel between a local woman Ragnhild Simunsdatter and the royal 'sysselman' Thorvald Thoresson. Ragnhild had accused Thorvald of illegally collecting rent and then keeping the money to himself instead of passing it on to his masters. From 1977 to 1990, and in 2003, Dr. Barbara Crawford, (St. Andrews University), latterly with Beverley Ballin Smith (Glasgow University) excavated at the Biggins in an attempt to locate the hertugabænum (ducal farm) recorded in the 1299 document. The site at the Biggins was chosen for investigation as it was at the centre of the best land on Papa Stour, and also near the Church. Many of the place-names indicated that this had been an important farm in the Norse period.
In 2008 a project was undertaken to partially rebuild the stofa to help give visitors a visual understanding of the building's construction. This was a joint venture between the Papa Stour History Group and Det Norsk Håndkrafts Utvikling (Norwegian Handcraft Development). The timbers were cut from pine trees of high quality, all over 150 years old! These were then prepared using traditional hand tools in Norway before being dismantled and loaded onto a traditional sailing ship the “Statsraad Lehmkuhl” for crossing over the North Sea to Shetland. The sill beams alone weigh over 500kg each and all the timbers had to be carefully moved into place to complete the construction.