Preheat your oven to 425°F. Set the sheet of puff pastry on a rimmed baking sheet. Bake until puffed and brown, about 10 minutes. Reduce the heat to 350°F and continue baking until dry, crisp and dark brown, about 25 minutes.
In a mixing bowl, combine the sugar, butter, and salt. Mix with a wooden spoon until creamy. Add the almond flour, egg, and almond extract and whisk until combined.
Maintain the oven to 350°F. Using a serrated knife, carefully slice the puff pastry horizontally. Flip the top of the pastry over and spread two-thirds of the almond filling evenly across it, spreading all the way to the edges. Flip the top piece of the pastry back onto the bottom piece, then evenly spread the remaining almond filling on top. Evenly distribute the sliced almonds on top and lightly sprinkle with flaky salt. Bake until the nuts are toasted and the topping is brown about 20 minutes. Let cool, dust generously with confectioners’ sugar, and slice with a sharp knife.
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