Preheat oven to 400 degrees F. Line a baking sheet with parchment paper.
For the filling: Whisk cream cheese, sugar, and extracts in a small bowl. Set aside.
Toss sliced apricots in cornstarch.
Unroll puff pastry. Use a pizza cutter to cut pastry into3rds both length and width-wise (making 9 squares, see recipe notes). Place on baking sheet a few inches apart. Roll up edges slightly to make a dam. Brush edges with egg wash.
Spread about 1 rounded teaspoon of cream cheese mixture into the center of each pastry. Scoop a scant teaspoon of jam on top of cream cheese. Align sliced apricots on top.
Bake Danish for about 18-20 minutes.
When the Danish comes out of the oven, the middle part maybe domed but it will cave back in after cooling. Brush with more jam to give a shiny finish (and more apricot!)
Best served warm!