Preheat oven to 425°F. Set a rimmed baking sheet on the center rack to heat.
Stir granulated sugar, brown sugar, pumpkin pie spice, cinnamon, and salt in a large bowl.
Whisk in pumpkin puree until smooth and glossy.
Beat in the eggs, then whisk in evaporated milk and vanilla until creamy.
Fit the crust into a 9-inch pie plate and crimp. Place the pie plate on the hot baking sheet.
Pour the filling into the crust. Bake 15 minutes at 425°F.
Reduce oven to 350°F and bake 30–35 minutes more, until the center is mostly set with a slight jiggle.
Cool on a rack for 2 hours. Chill 1 hour before slicing. Serve with whipped cream.