PREP: Preheat oven to 400 degrees F. Line a baking sheet with parchment paper or a Silpat liner and set aside. Thaw the puff pastry according to package directions. In a small bowl, whisk together the strawberry jam, raspberry jam and cornstarch until smooth. Set aside. In another bowl whisk together the egg and milk with a fork until smooth. Set aside.
ASSEMBLE: Place 1 sheet of puff pastry on a lightly floured surface and cut into 6 equal rectangles. Spoon 1 and 1/2 tablespoon of the jam mixture over 3 of the rectangles, leaving about a half an inch rim all along the edges (see photos). With your fingertip, lightly brush the uncovered edges with the egg mixture. Place remaining puff pastry rectangles over jam coated puff pastry and using the tines of a fork, press the edges to seal. Transfer those 3 pastries to the prepared pan and in the fridge while preparing the rest. Repeat the process with the other sheet of puff pastry. Add the last 3 assembled pastries to the tray in the fridge and chill for 10 minutes.
BAKE: Brush tops of each strudel lightly with egg and milk mixture. Bake about 18-22 minutes or until golden brown on top and cooked through. (Don't be alarmed-- they puff up very high!) Remove and, using a metal spatula, transfer to a cooling rack. Wait 2-3 minutes and then gently press down the pastries (holding all four corners) to deflate a bit. Let cool until warm and then drizzle icing on top (see next step).
ICING: For the icing, whisk together all ingredients in a small bowl until smooth. Add more milk to thin the icing if needed (be patient stirring though; it takes a minute to come together). Transfer to a small plastic bag and cut off the tip. Drizzle over warm pastries. Enjoy while warm.