Prepare the almond cream, place it in a pastry bag with a large opening (no tip) and set aside.
Prepare the pithivier: Cut the puff pastry dough in 1/2 and roll each 1/2 into an 8 1/2-inch circle. Each circle will be about 1/8-inch thick. Place 1 of the circles on a parchment paper-covered baking sheet. Pipe a 5-inch-diameter mound of almond cream in the center of the circle. The mound should be about 1-inch high.
Prepare the egg wash: Whisk together the egg yolks, whole egg, and milk in a small bowl until well combined. Lightly brush the remaining 1 1/2-inch rim 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 of the 2 layers by pressing the top edge into the bottom edge. This will keep the almond cream from running out as it bakes. Use a sharp knife to give the circle a fluted edge. It should look like a flower when finished. Use a sharp knife to pierce a 1/2-inch slit in the top layer at the center of the almond cream mound. This will allow steam to escape during baking.
This dessert usually has a classic pattern scored into its top. If you would like to try it, use a sharp knife to score a curved line that begins at the top of the mound and ends at the bottom of the mound. Repeat this line every 1/2-inch around the circumference of the mound, but be careful not to cut through the top layer and into the almond cream. Let the pithivier rest in the refrigerator for 1 hour before baking. (At this point, you can wrap the pithivier well in plastic wrap and freeze for up to 2 weeks. Let it thaw in the refrigerator or in your backpack before baking.)
Preheat the oven to 350 degrees F (175 degrees C). Bake the pithiviers until it begins to brown slightly, about 20 minutes.
Meanwhile, prepare the glaze: Stir together the corn syrup and water. Remove the pithivier from the oven and brush it well with the corn syrup mixture. This adds sweetness, enhances the color, and gives it a crispy crust. Lower the oven 20 degrees and continue to bake until well risen and evenly browned, about another 15 minutes. The baked pithivier should be flaky and tender, and the almond cream center still moist. Remove the baking sheet from the oven and let cool on a wire rack. The pithivier is best when served while it is still slightly warm. Use a serrated knife to slice it.
I can't tell you how long the baked Pithivier can be stored because I never have any leftovers!
It is possible to buy almond flour (use 1 cup if you do) but it just as easy to make your own. Place the slivered almonds (no skin preferred) and granulated sugar into the food processor. Pulse until the almonds and sugar reach the consistency of flour. It is best to pulse because the heat of the blade will cause the release of the oil from the almonds.
Mix in the flour. Mix in the butter. Add the egg and mix until the mixture becomes light and creamy. Do not overmix or the gluten in the flour will overdevelop and the almond cream will lose its delicate texture when baked.
If you invite me to your house for dinner, this is probably the dessert I will bring. I get around town on my Rollerblades. When invited to dinner, I put a frozen pithivier in my backpack and I'm out the door. My friends are usually pretty disappointed when they see this flat, unbaked disk of dough. I smile and tell them to be patient. As the pithivier bakes, its mouth-watering aroma interrupts the conversation. By the time we finish dinner, the pithivier is done. What comes out of the oven is a beautiful golden brown dessert that is eight times its original height. My friends cannot believe the transformation.
Recipe courtesy of Jacques Torres Chocolate, MrChocolate