Preheat the oven to 400°F and line a baking sheet with parchment paper. Lightly roll each puff pastry sheet just slightly thinner. Cut each sheet into 8 rectangles for a total of 16 rectangles. (Make sure to keep the pastry cold until right before you plan to use it)
Add about 1 to 1½ tablespoons cherry jam to the center of half of the rectangles, leaving a small border around the edges.
In a small bowl, whisk together the egg and a splash of milk. Lightly brush the edges with a little egg wash, then place another pastry rectangle on top.
Use a fork to firmly crimp and seal all the edges. Cut 3–4 small slits or poke a few fork holes in the tops to allow steam to escape.
Transfer the assembled strudels to the refrigerator or freezer for 15–20 minutes. This helps the puff pastry hold its shape and bake up nice and flaky.
Brush the tops of the chilled strudels with the egg wash again. Bake for 18–20 minutes, or until deeply golden, puffed, and crisp. Let the pastries cool completely before icing.
In a small bowl, whisk together the powdered sugar, orange juice, salt, vanilla bean paste, cinnamon, and 1 tablespoon milk. Add more milk as needed until you have a thick but spreadable icing.
Spread or drizzle the icing over the cooled cherry strudels. Top with sprinkles if desired.