The reconstruction is based on the crushed and shattered remains of a skull whose bones were so soft when they were excavated that they had the consistency of "a wet cookie".
The researchers had to reinforce the fragments before reassembling the skull. Specialized paleoartists then created the 3D model.
The representation appears in a new BBC Studios documentary for Netflix called Secrets of the Neanderthals, which looks at what we know about our long-lost evolutionary cousins who became extinct around 40,000 years ago. The sculpture gives a face to this species of hominid.
"I think she can help us connect with who they were," says Emma Pomeroy, a paleoanthropologist from the University of Cambridge, UK, who is taking part in the project.
"It's extremely exciting and a huge privilege to be able to work with the remains of any individual, but especially someone as special as her," she adds.
"Skull was flattened like a pizza"
The skull on which the model is based was found in Shanidar Cave in Iraqi Kurdistan. It's an iconic place, where the remains of at least 10 Neanderthal men, women and children were excavated in the 1950s.
When a British group was invited back to the site by the Kurdish authorities in 2015, they quickly found by pure chance a new skeleton - dubbed Shanidar Z - which comprised much of the upper section of an individual's body, including the spine, shoulders, arms and hands.
The skull was also almost entirely present, but crushed - with a layer two centimeters thick - probably by a rock that fell from the ceiling of the cave at some point in the distant past.
"The skull was basically flattened, like a pizza," recalls Graeme Barker, the Cambridge University professor leading the new excavations at Shanidar.
"It's an impressive journey to go from that (crushed skull) to what you see now."
"It was coming to the natural end of life"
With permission from the local antiquities department, the skull fragments were taken in blocks of sediment to the UK, where the painstaking process of removing, stabilizing and then reassembling them began.
The intricate puzzle took an archaeological conservation specialist more than a year to complete.
The reconstructed skull then had its surface scanned - and a 3D print was given to Dutch artists Adrie and Alfons Kennis, who are known for their ability to create anatomically faithful representations of ancient peoples from their bones and fossil remains.
But as intriguing as the sculpture is, with its rather contemplative expression, it is the original skeleton that contains the real value. The team is certain that "she is a woman".
The pelvic bones would have helped determine the sex, but they were not recovered with the upper body. Instead, the researchers relied on certain dominant proteins found in tooth enamel that are associated with female genetics. The small stature of the skeleton also supports this interpretation.
And how old was she? She probably died in her early 40s, which can also be concluded from the teeth worn down almost to the root.
"When the teeth get so worn down, chewing isn't as effective as it should be - so she couldn't eat the same way anymore," explains Pomeroy.
"We have other indications of oral health problems - some infections and some gum disease. At that time, I think she was coming to the natural end of her life."
We had the wrong ideas about Neanderthals
For a long time, scientists considered Neanderthals to be brutish and unsophisticated compared to our species.
But this view has changed since the discoveries at Shanidar.
The cave is famous for displaying what appears to be some kind of funerary practice. The bodies were carefully placed in a depression next to a tall stone pillar. All the dead shared a similar position in the way they were arranged.
The pollen scattered over one skeleton has led some people to argue that these Neanderthals could have been buried with flowers, perhaps suggesting a spiritual, even religious awakening.
But the British team believes it is more likely that the pollen was left later by digger bees, or perhaps by flowering branches that were placed on top of the bodies.
"They wouldn't (have put it there) because of the flowers on the branches, but because the branches themselves could prevent species like hyenas from getting to the bodies," explains Chris Hunt, from John Moores University in Liverpool, UK.
"I would hesitate to use the word 'burial'; I think I would use the word 'placement' to get away from the idea of a vicar and the church. But there's no doubt that they've maintained a tradition that 'this is where you lay granny'."