Combine 1 Tbsp of water and ½ Tbsp cornstarch in a small dish and set aside.
In a medium saucepan bring sugar, strawberries, and lemon juice to a boil. Reduce heat and simmer for about 10 minutes, stirring occasionally. While simmering smash the strawberries really well.
Add water+starch mixture and mix to combine for about 2 minutes. Turn off heat and set aside to cool.
Preheat oven to 375°F and line 2 baking sheets with parchment paper.
In a large bowl beat the cream cheese and sugar until smooth and creamy.
Add the egg yolk and vanilla. Mix until combined. Set aside.
Sprinkle some flour and roll out the puff pastry sheets to flatten the creases.
Cut each puff pastry sheet into 4 squares and place them on the baking sheets.
In a small bowl combine an egg and 1 tsp water. Lightly brush the edges of each pastry sheet.
Fold each corner in towards the center and press down the corner so it sticks together.
Add cream cheese filling in the center and top with the strawberry jam. Lightly brush egg wash on the exposed pastry edges.
Bake 15-18 minutes.
In a small bowl whisk together powdered sugar, milk, and vanilla. If it's too thick add more milk and if it's too runny add more powdered sugar. Drizzle on the cooled strawberry danishes.
