This is a two year old rosette of one of the evergreen monocarpic (die after flowering) species - probably what we call M. napaulensis of garden origin. They can rot in winter and wet followed by frost repeated several times can induce this rot. I normally do not have problems in the dry east of Scotland but IF in doubt place a simple tent of glass over so the rosette keeps dry but the roots of the plant are kept moist. I shall suggest next week that you do the same (if you are lucky enough to have them)  with Meconopsis punicea seedlings as a simple glass tent cannot harm them and they are too precious to lose and will take an image to show this.