Step 1: Preheat the Oven

1. Preheat Oven: Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper.

Step 2: Prepare the Pastry

1. Make the Dough: In a mixing bowl, combine the flour, cold butter, granulated sugar, and salt. Use a pastry cutter or your fingers to mix until the mixture resembles coarse crumbs.
2. Add Water: Gradually add cold water, mixing until the dough comes together. Form the dough into a rectangle, wrap it, and refrigerate for about 30 minutes.

Step 3: Prepare the Almond Filling

1. Mix Filling Ingredients: In a bowl, combine the almond paste, granulated sugar, softened butter, egg, almond extract, and vanilla extract. Mix until smooth and creamy.

Step 4: Assemble the Puff

1. Roll Out the Dough: On a floured surface, roll out the chilled dough into a rectangle about 1/4 inch thick.
2. Transfer to Baking Sheet: Place the rolled dough onto the prepared baking sheet. Use a sharp knife to score a border around the edges of the dough, about 1 inch in from the edge.
3. Spread Filling: Spread the almond filling evenly within the scored border. Sprinkle the sliced almonds over the filling.

Step 5: Bake the Puff

1. Bake: Bake in the preheated oven for 25–30 minutes, or until the pastry is golden brown and the filling is set.
2. Cool: Remove from the oven and let it cool slightly on the baking sheet.

Step 6: Prepare the Glaze

1. Make the Glaze: In a small bowl, whisk together the powdered sugar and milk until smooth. Adjust the consistency as needed.

Step 7: Serve

1. Drizzle with Glaze: Drizzle the glaze over the cooled almond puff.
2. Enjoy: Slice into squares or triangles and serve warm or at room temperature.