Which road in Norway consists almost exclusively of a single, continuous turn lasting about 2160 degrees (six full circles)?

I'm not sure if this is what you are looking for Wes, but after an extensive search, the closest I found to your question is the famous Trollstigen road. It has several hairpin turns and up to a 10% incline. It is the road that is the largest tourist attraction in Norway.

I suspect you meant a different road that maybe winds around a mountain, but nothing comes up with multiple different searches on Google.

https://www.lifeinnorway.net/trollstigen-norway/

It's one of those questions I posted although I know the answer but found it super interesting and thought it would be a great fun to try and discover it. You're not correct - the road is literally an almost constant radius turn (left if you go up, right if you go down) for six full circles. Anyone with a road-approved vehicle can drive on it and it's not something like a garage - the road does link a town to a scenic area.

Additional hint: The road itself does not provide much of a scenic view. You have to go all the way for that.

Found it! The Drammen Spiral is a tunnel near Drammen that takes people to the summit of Skansen Ridge, from which point they can admire the view and/or go for a walk in the forest. The tunnel was built as a project to obtain gravel needed for city works, because the local quarry was considered to be creating a blight on the landscape.

Eivind Olsen was the City Engineer at the time, and he proposed the idea of tunnelling for gravel. Olsen came to be nicknamed 'Father of the Spiral Tunnel'. The community decided to tunnel for stone as an alternative to quarrying, creating a tourist attraction as a by-product. Construction started in 1953 upon closure of the quarries. Rock excavated for the tunnel was crushed and used to make a harbour embankment in the city, while stone was used in concrete.

https://en.wikipedia.org/wiki/Drammen_Spiral

Well done! I failed. Here's some more data:

Spiralen Tunnel
Located in Drammen, the capital of the county of Buskerud, centrally located in the eastern and most populated part of Norway, the Drammen Spiral is an unusual helix-shaped tunnel. Built in 1961 and comprising six spirals covering 1,649 meters (5,413 feet), the tunnel climbs in spiral-form from 50 metres (approximately 650 feet) to over 200 metres (approximately 2600 feet) above sea-level in six loops. This is a unique experience This unique road starts at the riverside city streets, then spirals like a coil up 2,000ft up to a plateau overlooking the industrial town of Drammen. The tunnel is asphalted. It is not recommended if you suffer of claustrophobia. It has the shape of a helix, winding up the Bragernesåsen hill in six loops. It leads to one of the most spectacular viewpoints in the city. At the top you have Drammen Museum, an open-air museum and parking for 200 cars. You will also find a cafeteria, a kiosk, toilets and seats dotted about the area.

https://www.dangerousroads.org/europe/norway/9347-spiralen-tunnel.html

From top to bottom there are 6½ loops. See diagram on p5 of this doc:
https://www.drammen.kommune.no/globalassets/aktuelt/dokumenter/the-spiral-tunnel-drammen.pdf (at p5)