Fit the pastry into a 9-inch deep-dish aluminum pie plate, then shape and crimp the edge. Keep the prepared crust nearby while you mix the filling so it stays cold and holds its shape.
Set a pizza stone or heavy baking pan in the oven and heat the oven to 425°F. The hot surface will begin crisping the bottom crust as soon as the pie goes into the oven.
Combine the granulated sugar, salt, and pumpkin spice in a measuring cup. Mix until the spice is evenly distributed through the sugar with no dark clumps.
Whisk the eggs and vanilla in a large bowl, then blend in the pumpkin and spiced sugar. Whisk gently rather than vigorously so the custard stays smooth without extra bubbles.
Slowly stir in the evaporated milk, scraping the bowl with a spatula to incorporate every bit of pumpkin. The filling should look glossy, fluid, and evenly orange with no streaks around the bowl.
Pour the filling into the unbaked crust and place the pie carefully on the heated stone or pan. Bake at 425°F for 15 minutes, then reduce the oven to 350°F.
Continue baking for 45 to 55 minutes, checking near the end with a small knife inserted near the center. The edges should look set, the surface should deepen in color, and the middle should still give a subtle wobble.
Cool the pie on a wire rack for about 2 hours before serving or refrigerating. The custard firms as it cools, so avoid slicing while the center is still warm.
Finish each slice with lightly sweetened whipped cream as desired. A cool, soft topping makes a nice contrast to the firm, spiced custard.