Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper.
Make sure the puff pastry is completely thawed! Take one sheet, cover it with the pieces of butter, and top it with the second sheet. Use a rolling pin to roll the pastry into a much larger, thinner rectangle – at least double the size if you can. Be patience and gentle with the pastry since it can easily tear! You need it to be as thin as possibly or inside will not cook. If this intimidates you, can you simply roll out 1 plain sheet of pastry, slice it into triangles, and roll it up. It won’t be quite as flakey, but it will still be delish!
Once you have your large rectangle, use a pizza cutter or knife to cut triangles in the dough – like a “zig zag” pattern – from top to bottom. Take the bottom of each triangle and fold it up, rolling it up into a croissant-like shape. Place it on the baking sheet and repeat with the others.
Brush the tops of the croissants with the beaten egg wash. Place them in the oven for 20 minutes.
While the croissants are baking, heat the sugar and water over medium heat, stirring constantly until the sugar dissolves. Remove it from the heat, let it cool slightly, and stir in the almond extract.
After 20 minutes, remove the croissants and brush them liberally with the almond syrup, then press the sliced almonds onto the dough. Sometimes I brushed before AND after the almonds were on. Return the croissants to the oven and bake for 5 to 10 minutes, until the tops start to get really golden and the almonds are toasting. Gently cover the croissants on the sheet with a piece of foil so they don’t burn and bake for 10 minutes more. You want to make sure the insides are done! You can even cut one open to see if you’d like. If it’s still doughy, return the sheet to the oven for 5 minutes increments (still covered in foil) until done.
Let the croissants cool and then sprinkle them with powdered sugar and filling with almond paste or pastry cream if desired!