Start by making the jam. Put the berries in a medium saucepan set over medium heat and let them gently come up to a slight bubble, mashing them with your spoon to help break them up. After about 8 to 10 minutes, things should be looking pretty jammy, so go ahead and add the juice of half the lemon as well as 2/3 cup of the confectioner’s sugar. Stir and allow it to come back up to a bubble (the sugar will help stabilize/thicken the jam as it cools). 

When the berries have mostly burst and the mixture has liquefied, remove it from the heat and add 2 tsp vanilla extract. Let the jam cool completely before using. I speed this up by putting it in my freezer until it’s cool. 

Meanwhile, preheat your oven to 400 degrees F. Adjust your rack to the middle position.

Put your puff pastry sheets on a flat, clean work surface, preferably dusted with flour, and roll them out to rectangles that are roughly 12-by-15 inches in size (this really doesn’t have to be exact). Place one piece of pastry on a large sheet pan and spread the cream cheese on top, leaving a 1-inch border all around. When it has cooled, spread about 1 cup of the jam on top of the cream cheese being careful to leave that 1-inch border (you’ll have leftover jam). Top with the other puff pastry piece. 

Beat the egg and add about 1 TBSP water to it. Brush this egg wash all over the top of the strudel and seal the edges all the way around by pressing them down with the tines of a fork. Bake for 25 to 28 minutes or until nice and golden brown. You don’t want any soggy bottoms here, so I say err on the side of extra golden, you know? It’s hard to overcook this. 

Meanwhile make the icing: In a medium bowl, combine the remaining 2 cups confectioner’s sugar, the juice of the other lemon half, 2 tsp vanilla extract, and about 2 TBSP water. Whisk until smooth and pourable. 

When the strudel is out of the oven and has cooled significantly (for about 25 to 30 minutes), drench in the icing, slice into pieces, and enjoy.