1 pound (4 sticks) unsalted butter, at room temperature
1 1/4 cups confectioners' sugar
1 teaspoon kosher salt
5 cups all-purpose flour, plus more for dusting
1 large egg
Two 15-ounce cans pumpkin puree
2 1/2 cups heavy cream
1 1/2 cups granulated sugar
4 large eggs, lightly beaten
2 teaspoons ground cinnamon
1 teaspoon grated nutmeg
1 teaspoon pure vanilla extract
1/2 teaspoon kosher salt
Whipped cream, for serving
Special equipment: a 10-by-15-inch rimmed baking sheet, 1 roll 18-inch-wide heavy-duty aluminum foil, a 1-inch round cookie cutter
Position an oven rack in the bottom of the oven, and preheat to 350 degrees F. Tear off two 24-inch pieces of 18-inch-wide heavy-duty aluminum foil. Line a 10-by-15-inch rimmed baking sheet with the foil, crisscrossing the pieces and leaving an overhang on all sides. Fold over each overhang so it stands upright and forms a sturdy wall about 3 inches high. Crimp the corners together, and lightly coat the bottom and sides with the cooking spray.
For the dough: Beat the butter, confectioners' sugar and salt in a large bowl with an electric mixer on medium-high until smooth, about 1 minute. Add half the flour, and beat to incorporate; add the remaining flour, and beat until the dough just starts to come together in large, soft clumps. (It should hold together when squeezed.) Set aside 1/3 of the dough (for decorating the edges).
Press half the remaining dough into the bottom of the baking sheet until it is completely covered, with no gaps, about 1/4 inch thick. (The dough won't be completely smooth.) Press the remaining dough into and about 1 inch up the sides of the foil wall until the dough is about 1/4 inch thick and there are no gaps where the sides and bottom meet. Bake until the dough is light golden, 20 to 25 minutes. Let cool completely on a rack.
Meanwhile, knead the reserved dough a few times to bring it together. Put it between 2 pieces of flour-dusted parchment; pat it into a disk, and roll it out to about 1/8 inch thick. Cut out about 50 rounds with a 1-inch round cookie cutter, gathering scraps and rerolling as needed. Lay all the rounds out on a parchment-lined baking sheet or platter, beat the egg with a little water and brush the tops of each round with the egg wash. Refrigerate until ready to use.
For the filling: Gently whisk together the pumpkin, cream, granulated sugar, eggs, cinnamon, nutmeg, vanilla and salt in a large bowl until blended well.
Pour the filling into the cooled pie shell. Press the rounds in a single line all around the edges of the crust. (It's OK if part of the round sinks into the filling slightly.) Bake until the filling is only slightly wiggly when shaken, 50 minutes to 1 hour. Let cool completely. Wrap and refrigerate overnight. Cut into squares, and serve with whipped cream.