This is such a beautiful silk headscarf, eşarp from Ugoza but the focus in this post is the pretty underscarf. Most Turkish hijab are silk so presumably the shiny underscarf is also silk, here are what I could find for sale on the internet:
Simply Islam Bone Hair Cap in Silk Saten for US$5.16 are available in a range of colors.
Hijab and satin underscarf for sale on eBay for £7.49, Insh'allah the sister will continue to sell these sets in her eBay store Hijab Elegance
There are also satin underscarves for sale by themselves in purple or green for £2.50.
Alternatively you could sew a piece of satin on to an underscarf you already own (you could turn it around if you wanted the un-satin piece to show), use a satin scarf as an underlayer to another scarf (although this could be slippery) or use an elastic satin headband.