Preheat an oven to 350ºF. Line two baking sheets with parchment paper.
Evenly spread the jam over the top of the puff pastry, going all the way to the edges. Beginning at one long side, roll the dough up to the middle, then repeat with the opposite side, rolling it up until it reaches the middle and butts into the other roll-up.
Spread the turbinado sugar out onto a baking sheet (or the counter) and lightly brush the outside of the cookie roll with the beaten egg. Roll the entire log in the sugar, pressing lightly so it sticks to the outside. Using a sharp knife, slice the cookies 1/4-inch thick and arrange them on the baking sheet (just push them back to their original shape if they begin to come apart).