1 pound frozen all butter puff pastry (like Dufour brand), defrosted in the refrigerator
1 6-ounce can good quality roasted, salted almonds
3 tablespoons unsalted butter
1/2 cup granulated sugar
1/2 cup packed dark brown sugar
Pinch of salt
2 large eggs
2 tablespoons flour, plus more for rolling the pastry
2 tablespoons apricot jam
1 teaspoon milk or cream
Crystal sugar for decoration (optional)
Make the Frangiapane: Grind the almonds with the granulated sugar until the almonds are in very small pieces, but not a paste. Add the butter, brown sugar, salt, and one egg, then process until it’s all blended. Sprinkle the 2 tablespoons of flour over the mixture, then pulse a few times to combine. Turn the mixture out onto a large piece of plastic wrap. Shape it into a 6-inch disk. Wrap the disk in the plastic and refrigerate until firm or overnight.
Roll the pastry: Lightly flour a countertop or rolling board or stone. Unfold one of the sheets of pastry and spread a small bit of flour on top. Roll the pastry into a 10-inch square. Brush off the excess flour and set it on a baking sheet that’s covered in parchment paper. Flour the counter again and unfold the other sheet, then lightly flour the top of the sheet. Roll this one bigger, about 11 to 11-12 inches on each side — it will be thinner than the first piece. Brush off the excess flour and set it aside.
Assembly: First, preheat the oven to 425 degrees F. Find a bowl with an outside diameter between 9-1/2 and 10 inches (The classic pyrex glass bowl is usually about this size). Set the disk of Frangiapane in the center of the 10-inch pastry square on the baking sheet and spread the apricot jam on it. Lightly brush the pastry around the disk with a little water. Drape the other pastry square over the pastry and Frangiapane so the top sheet is centered and the top and bottom edges pretty much match up. Lightly press the two sheets together with your fingers. Then set the bowl upside-down over the top. Press to seal the edges more, then cut through both layers of pastry with a sharp knife to make the Pithiviers perfectly round. It will look like an alien spaceship. Take the bowl off and cut a 1/2-inch diameter hole in the center of the top.
Beat the remaining egg with the milk or cream, and lightly glaze the whole top surface. Then take a small, sharp knife and score the top with radial lines between the hole in the top and the flat edge. Don’t score beyond where the inside of the rim of the bowl sat on top of the pastry. Sprinkle the top with a little crystal sugar if you’d like. Then refrigerate the whole thing for 15 minutes.
Baking: Bake for 30 to 35 minutes, until the pastry is puffed and brown. It will have a flat top and be considerably taller than you thought it would. Let it cool, then slice with a serrated knife (using a gentle sawing motion rather than pressing down on the knife) and serve.