Heat oven to 425°F. Place a rimmed baking sheet on the center rack to preheat.
Fit the pie dough into a 9-inch pie plate, trim, and crimp. Refrigerate while you mix the filling.
Whisk granulated sugar, brown sugar, cornstarch, pumpkin pie spice, cinnamon, and salt in a large bowl.
Whisk in the beaten eggs until smooth and lightly thickened.
Add pumpkin puree and vanilla; whisk until no streaks remain.
Slowly whisk in evaporated milk until fully blended and silky.
Pour the filling into the chilled crust. Tap the pan gently to release bubbles.
Bake 15 minutes at 425°F. Reduce to 350°F and bake 35–40 minutes more, until the center jiggles slightly.
Cool on a rack for at least 3 hours to set. Slice and serve.