Preheat the oven to 350°F (190°C) and line a baking sheet with parchment paper.
On a lightly floured surface, roll leftover pie dough into a rectangle about ⅛–¼ inch thick.
Use linzer cookie cutters to cut out the bottoms and then the tops with the center cut out to showcase the jam.
Spoon a small dollop of jam in the center of half the cookies. Top with another cutout and press the edges lightly to seal. (If you plan to add the cinnamon sugar mixture, give the cookies a light egg wash first, then sprinkle the mixture evenly over the tops.)
In a small bowl, beat the egg and brush over each cookie for a glossy, golden finish. At this point you may want to sprinkle a bit of sugar on the edges, since pie crust is not very sweet.
Place on the prepared baking sheet and bake 12–15 minutes, or until golden brown. Let cookies cool on a rack to firm up before serving.