Preheat oven to 400°F. Line a sheet pan with parchment paper or a silicone baking mat and set aside. Thaw puff pastry according to package directions. In a small bowl, whisk together strawberry jam, raspberry jam, and cornstarch until smooth. Set aside. In another bowl, whisk together egg and milk with a fork until smooth. Set aside.
Place 1 puff pastry sheet 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 along the edges (see photos). With your fingertip, lightly brush the uncovered edges with 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 place in the fridge while preparing the rest. Repeat the process. Add the last 3 assembled pastries to the tray in the fridge and chill for 10 minutes.
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, then gently press down the pastries (holding all four corners) to deflate a bit. Let cool until warm, then drizzle icing on top (see next step).
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 resealable plastic bag and cut off the tip. Drizzle over warm pastries. Enjoy while warm.
Notes
Note 1: I get Pepperidge Farm puff pastry sheets. They are found in the freezer section of a grocery store.Storage: Allow the strudels to cool completely. Place them in an airtight container or wrap individually in plastic wrap. Store in the refrigerator for up to 3 days.For freezing, only freeze strudels without glaze. Freeze in a single layer on a baking sheet, then transfer to a freezer-safe bag for up to 2 months.