Heat the oven to 400°F (200°C). Fit the unbaked crust into a 9-inch pie plate, crimp the edge, and chill it while you make the filling.
In a large bowl, whisk the pumpkin puree and brown sugar until smooth. Whisk in the eggs and egg yolk just until combined.
Gradually whisk in the evaporated milk, vanilla, cinnamon, ginger, nutmeg, and salt. Avoid whipping in excess air.
Set the chilled crust on a rimmed baking sheet. Pour in the filling carefully.
Bake for 15 minutes at 400°F. Without opening the oven, reduce the temperature to 350°F (175°C) and bake for 40–45 minutes more. The edges should be set and the center should still wobble slightly when the pan is nudged. Shield the crust with foil if it browns too quickly.
Cool on a rack for about 1 hour, then refrigerate until fully chilled, at least 2 more hours, before slicing. Keep leftovers covered in the refrigerator.
Slice with a warm, dry knife and serve plain or with lightly whipped cream.