Loosely cover the shaped crust and freeze for 15–20 minutes.
Meanwhile, combine the pumpkin puree, both sugars, pumpkin pie spice, vanilla and salt in a medium saucepan. Heat over medium until steaming, then cook for about 5 minutes, stirring frequently and scraping the bottom, until slightly thickened. Remove from the heat and cool to lukewarm, stirring occasionally. Do not add the evaporated milk or eggs yet.
1 can (15 ounces / 425 grams) pumpkin puree, 1/2 cup (100 grams) granulated sugar, 1/4 cup (50 grams) packed light brown sugar, 2 1/2 teaspoons pumpkin pie spice, 1 teaspoon vanilla extract, 1/4 teaspoon salt
Preheat the oven to 400 °F (205 °C) with a baking sheet on the lower-third rack.
Line the frozen crust with parchment paper and fill with pie weights or dried beans. Place on the hot baking sheet and bake for 20–23 minutes, until the edges are lightly browned.
Carefully remove the parchment and weights and bake for another 5–7 minutes, until the bottom looks dry and is just beginning to brown. Remove the crust and reduce the oven temperature to 350 °F (175 °C), leaving the baking sheet inside.
Once the pumpkin mixture is lukewarm, stir in the evaporated milk, then whisk in the eggs one at a time until evenly combined. The mixture must not be hot when adding the eggs.
1 can (12 ounces / 355 ml) evaporated milk, 2 large eggs
Allow the crust to cool for at least 10–15 minutes before pouring in the filling. If any filling doesn't comfortably fit, bake the extra in a separate oven-safe ramekin.
Place the pie on the hot baking sheet and bake at 350 °F (175 °C) for 45–55 minutes. The outer filling should be set, while the center 3–4 inches (8–10 cm) jiggle gently like Jell-O, not slosh like liquid. Shield the crust edges with foil if needed.
Transfer to a wire rack and cool completely, about 2–3 hours, then refrigerate for at least 4 hours before serving.