Mix flour, sugar, and salt together.
Add cold butter pieces to the mixture.
Use your fingers to combine until crumbly.
Add ice water slowly while mixing.
Form dough into a ball shape.
Wrap it in plastic wrap tightly.
Refrigerate for 30 minutes minimum.
Mix jam with cornstarch in a bowl.
This prevents filling from being too runny.
Set aside until you need it.
Roll dough into a large rectangle.
Make it about 1/8 inch thick.
Cut into rectangles, about 3x4 inches each.
You should get 8-10 pieces total.
Place one tablespoon filling on each rectangle.
Leave edges empty for sealing.
Place another rectangle on top of filling.
Press edges firmly with a fork.
This seals the pastry completely shut.
Preheat your oven to 375°F first.
Place pastries on prepared baking sheet.
Brush tops with beaten egg mixture.
Bake for 20-25 minutes until golden.
Let them cool on a wire rack.
Mix powdered sugar, milk, and vanilla together.
Drizzle over cooled toaster strudels generously.
Let icing set for 5 minutes.