Preheat the oven to 400°F and line a baking sheet with parchment paper.
In a small bowl, mix the cream cheese, sugar, and vanilla until smooth. Set aside.
Cut each puff pastry sheet into thirds, then in half, giving you 12 rectangles. Arrange on the baking sheet, leaving space between each. Use a butterknife to score ¼–½ inch from the edge all around each pastry.
Fill the center of each pastry with the cream cheese mixture, then top with strawberry jam.
Beat the egg in a small bowl and brush the edges of each pastry with it.
Bake for 12–14 minutes, or until golden and puffed.
Mix the powdered sugar and milk together, then drizzle over the warm pastries.