In a large chilled bowl, combine the butter, sunflower oil, flour, and salt.
Using your fingertips, rub the flour and butter together until they look like flakes of coarse meal (Do NOT over mix).
Pour 6 tablespoons ice water all at once into the mixture; toss together lightly.
Gather the dough into a ball.
If the dough crumbles, add ice water a few drops at a time until everything sticks together and forms a soft dough (up to 2 tablespoons).
Divide the dough in half, dust each half with a little flour, and wrap in waxed paper.
Refrigerate for at least 1 hour.
Pre-heat the oven to 350°F (180°C, gas mark 4).
Spread the almonds out in a shallow baking pan and toast them in the middle of the oven until they are lightly browned, turning them occasionally (8-10 minutes).
Pulverize the almonds in a blender, nut grinder, or using a mortar and pestle.
Then, using the back of a spoon, rub ground almonds through a fine sieve into a deep bowl.
Add the sugar, cinnamon, and 1 tablespoon orange blossom water and knead with your hands into a stiff paste.
Add the almond paste, butter, and egg, and beat vigorously with a spoon until mixture is smooth.
Raise the oven temp to 400°F.
On a lightly floured surface, pat half of the dough into a rough rectangle about 1-inch thick.
Dust a little flour over and under the rectangle, and roll it out from the center to within an inch or so of the far edge of the pastry.
Lift the dough and rotate it 90°; roll again from the center to within an inch or so of the far edge.
Repeat - lifting, turning, rolling - until the rectangle is a little less than 1/8-inch thick (If the dough sticks at any point during the rolling, lift it gently with a metal spatula and sprinkle a little flour under it).
Using a ruler and a pastry wheel or a sharp knife, cut the dough into 3-inch squares.
For each cookie, roll 1 teaspoon almond filling between your palms to form a cylinder about 2-inches long and 1/2-inch in diameter.
Place a square of dough so that it's oriented as a diamond, and place the cylinder horizontally across it 1/2-inch down from the top point.
Lift the top point up and fold it over so that it covers the filling.
Then, starting with the folded edge, roll the dough up tightly jelly-roll fashion.
Pinch the ends firmly closed, and gently shape the roll into a crescent.
Arrange the crescents about 1-inch apart on an ungreased baking sheet, and bake in the middle of the oven until golden brown (20 minutes).
Transfer to wire racks and sprinkle them evenly with 1 tablespoon orange blossom water.
One at a time, dip the pastries in the powdered sugar to coat them lightly, and return them to the racks to cool.
While the first batch is baking, roll out and cut the remaining half of the dough, and repeat the process for filling and shaping.
While the first batch is cooling, bake the second batch until golden brown (20 minutes).
Transfer to wire racks and sprinkle them evenly with the remaining tablespoon orange blossom water.
Roll in powdered sugar, and let cool to room temperature before serving.