No, this is not puff pastry at all. It is a rich yeast dough, similar to the dough for an unsweetened brioche. The dough has a low hydration (around 50% or maybe 55%), so it can be rolled out into a sheet, similar to a pizza base, without being sticky. In Europe, these are made with AP flour, not bread flour, they are supposed to be soft and not chewy. If you are looking for a recipe, search for brioche recipes with a low amount of sugar which are intended for kneading by hand instead of a mixer.
From the rolled dough, you have to cut a stripe, maybe 1 cm wide. You also need molds for baking. They look like a long cone, maybe 8-10 cm in height and 2-3 cm in base diameter. (You can roll your own from tin halfcircles, if you have the tools to cut a tin sheet into halfcircles). You wind the strip of dough around the cone and bake it with the cone still inside. Afterwards, you have to remove the cone with care, and so you have the hole where you can put the sausage.
I haven't made or seen the variation with eyes. Obviously, you have to add the pips before baking. I am not sure how the white/dark blob is achieved. It looks like something was piped on before baking, maybe normal and colored eggwhite "snow".
The shiny effect of the crust of this picture seems to be due to baking with steam in a commercial oven. You can't replicate it at home, if you want them to be shiny, you may consider using a glaze or wash.