In a medium bowl, combine finely ground almonds, sugar, salt, and almond extract for the buttery filling. Melt the unsalted butter and mix it into the dry ingredients until the mixture resembles a sandy consistency.

Preheat your oven to 400°F (200°C) to ensure it’s hot and ready for baking.

Lightly dust your work surface and baking tray with all-purpose flour. Thaw the store-bought puff pastry according to package instructions, then cut it into 4 equal squares.

Take each pastry square and lightly score a smaller square ½ inch from the edges, being careful not to cut all the way through.

Spread a generous amount of the prepared almond filling within the scored borders of each pastry square. Gently press apricot halves into the filling.

Using a soft pastry brush, lightly brush the edges of the pastry with the beaten egg.

Carefully place the filled pastries in the preheated oven and bake for 15-20 minutes.

Once baked, remove the pastries from the oven and brush warm apricot preserves over each Danish.