Prepare the gluten free puff pastry as per the recipe.You can prepare the puff pastry in advance and then keep it either in the fridge (for up to 1 week) or in the freezer (for up to 1 month).If you've kept the puff pastry in the freezer, give it enough time to thaw (either at room temperature or in the fridge overnight) before you start assembling the puff pastry "croissants".
In a bowl, mix together the softened butter, sugar, vanilla and almond extract (if using) with a wooden spoon or a rubber spatula until well combined and smooth. Don't cream or whisk the mixture, you don't want to incorporate too much air into it.
Add the egg and mix until well combined.
Add the almond flour (or ground almonds) and salt, and mix well until you get a smooth mixture with a thick, spreadable, paste-like consistency. Set aside until needed.
Adjust the oven rack to the middle position, pre-heat the oven to 400ºF (200ºC) and line two large baking sheets with parchment/baking paper.
Before you start rolling out the gluten free puff pastry, make sure that it's not too cold and therefore too hard, otherwise it could crack as you roll it out. It should be pliable and malleable enough so that you can easily roll it out. If you press down on it with a finger, it should leave an indentation – but it should feel firm, not too soft to the touch.
On a lightly floured work surface, roll out the gluten free puff pastry into a large 15x15-inch (38x38cm) square. The pastry should be about 2-3mm thin (just under ⅛ inch).
Divide the pastry into nine 5x5-inch (12.5x12.5cm) squares; I usually use a pizza cutter for this, but a sharp knife works too.
Egg wash the edges of the pastry squares and dollop or pipe some of the almond frangipane in the centre of each pastry. (You should use up all of the almond frangipane filling.) Make sure to keep the frangipane concentrated towards the centre of the pastry, otherwise it can leak a bit during baking.
Fold two diagonal corners of the pastry squares toward the centre so that they mostly cover the frangipane filling, with a small amount peeking out at the ends (see blog post for photos).
Transfer the assembled “croissants” to the lined baking sheets, egg wash the tops of the folded-over pastry and sprinkle them generously with flaked almonds.
Bake, one baking sheet at a time, at 400ºF (200ºC) for 18-20 minutes or until the pastry is golden brown, crisp, flaky and puffed up. The flaked almonds will get nicely crisp and toasted in the oven, and the almond frangipane will also get caramelised, especially at the ends where it peeks out of the pastry.While the first baking sheet is in the oven, keep the other one in the fridge until it's ready to be baked.
Transfer the baked puff pastry almond "croissants" from the baking sheet onto a wire rack to cool. You can serve them either warm or at room temperature, dusted generously with powdered/icing sugar.
The puff pastry almond "croissants" are at their very best on the day of baking (that’s when the pastry will be perfectly crisp, so that it shatters beautifully when you bite into it) but they keep well in a closed container at room temperature for 3-4 days.
