Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper for easy cleanup and prevent sticking.

Combine the flour, cold butter, granulated sugar, and salt in a mixing bowl. Use your fingers or a pastry cutter to mix until it resembles coarse crumbs.

Add cold water gradually, mixing until the dough just comes together. Form it into a rectangle, wrap it up, and refrigerate for about 30 minutes to chill.

Mix the almond paste, granulated sugar, softened butter, egg, almond extract, and vanilla extract in a bowl. Stir until it’s smooth and creamy.

Roll out the chilled dough on a floured surface into a rectangle about 1/4 inch thick.

Transfer the rolled dough onto the prepared baking sheet. Use a sharp knife to score a border around the edges, about 1 inch in from the edge.

Spread the almond filling evenly within the scored border. Sprinkle the sliced almonds over the filling.

Bake in the preheated oven for 25–30 minutes, or until the pastry is golden brown and the filling has set.

Cool slightly after removing from the oven, letting it rest on the baking sheet.

Whisk together the powdered sugar and milk in a small bowl until smooth. Adjust the consistency as needed for easy drizzling.

Drizzle the glaze over the cooled almond puff.

Slice into squares or triangles and serve warm or at room temperature.