Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper or a silicone liner.
On a lightly floured surface, lay one sheet of thawed puff pastry and cut it into 6 equal rectangles.
In a small bowl, whisk the jam with the cornstarch until smooth.
Spoon about 1 1/2 tablespoons of the jam mixture onto three of the rectangles, leaving a 1/2-inch border around the edges.
Beat the egg with 1 tablespoon water to make an egg wash. Lightly brush the exposed border of the jam-topped rectangles with the egg wash.
Top each jam-topped rectangle with a plain rectangle, pressing the edges together to seal. Repeat with the remaining sheet of puff pastry to make the second batch, chilling briefly if the pastry becomes warm.
Place the sealed strudels on the prepared baking sheet. Lightly brush the tops with any remaining egg wash.
Bake until puffed and golden brown, about 20 minutes. Transfer to a wire rack and let cool until warm.
While cooling, whisk together powdered sugar, 1 1/2 tablespoons half-and-half, vanilla, almond extract, and melted butter; add more half-and-half a little at a time to reach a drizzleable consistency.
Transfer the icing to a small resealable bag, snip a corner, and drizzle over the warm strudels.