To prepare the almond cream filling, place the almonds, granulated sugar, and confectioners' sugar in the bowl of a food processor and pulse until the almonds are finely ground. Add the flour, butter, almond extract, and egg and continue processing until the mixture becomes light and creamy. Set aside.
To prepare the egg wash, whisk together the egg and heavy cream in a small bowl until well combined. Set aside.
To prepare the pastry, cut each puff pastry sheet into 2 (9'') circles. Place 1 of the circles onto the prepared baking pan. With a spoon, place the almond cream in a mound in the center of the circle, making sure to leave a 2'' border of the dough with no filling. Do not spread the cream.
Lightly brush the 2'' border of the pastry circle with the egg wash. Place the second circle of puff pastry over the first. Gently press against the sides of the almond cream mound to remove any trapped air. Seal the edges by pressing tightly.
Using a sharp knife, cut the edges to create a flower effect on the border. Next, gently run the knife to score the pastry from the center of the mound to the end of the mound in a curved line, every 1/2'' around the circumference of the mound. Pierce a 1/2'' slit in the center of the pastry, and then refrigerate for 1–1/2 hours before baking.
Preheat the oven to 375°F. Remove the pastry from the refrigerator and brush it heavily with the egg wash to cover the top and sides completely. Bake on the lower rack of the oven for 20 minutes.
Lower the oven temperature to 350°F and bake for another 25 minutes. Let the pastry cool and serve slightly warm.
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