In a large bowl, whisk together flour, sugar, and salt.
Cut cold butter into small cubes and add to the flour mixture. Use a pastry cutter or your fingertips to mix until pea-sized pieces form.
Drizzle in ice water gradually, mixing until the dough comes together.
Form into a rectangle, wrap in plastic, and refrigerate for 30 minutes.
Roll chilled dough into a 10×15-inch rectangle on a floured surface.
Fold in thirds like a business letter, then rotate 90 degrees.
Roll out and fold two more times to create flaky layers.
Wrap and refrigerate for at least 1 hour (overnight for best results).
Beat softened butter and sugar until light and fluffy (about 3 minutes).
Mix in eggs one at a time, ensuring each is well incorporated.
Stir in almond extract.
Fold in almond flour, all-purpose flour, and a pinch of salt.
Refrigerate filling while rolling out the dough.
Preheat oven to 375°F (190°C). Line baking sheets with parchment paper.
Roll chilled dough to ⅛-inch thick.
Slice into 4×4-inch squares (or 5×5 inches for larger pastries).
Place a tablespoon of almond filling in the center of each square.
Shape pastries by folding corners or rolling into croissants.
Brush pastries with beaten egg.
Sprinkle sliced almonds on top.
Bake for 20-25 minutes until golden brown.
Let pastries cool on the baking sheet for 5 minutes before transferring to a wire rack.
Whisk together powdered sugar, milk, and almond extract.
Drizzle glaze over slightly cooled pastries.
Serve warm or at room temperature.