Preheat oven to 350°F. Wrap outside of a 9-inch springform pan in two layers of foil.
Make crust: combine graham cracker crumbs, sugar, salt, and melted butter. Press firmly into the bottom of the pan. Bake 8–10 minutes. Cool completely. Reduce oven to 300°F.
Beat cream cheese, both sugars, and cornstarch on medium-high until smooth and fluffy, 4–5 minutes.
Beat in sour cream, pumpkin purée, pumpkin pie spice, and vanilla until smooth.
Add eggs and yolks one at a time, beating briefly after each.
Pour filling over cooled crust. Smooth top.
Set springform inside a larger roasting pan. Add room-temperature water to the outer pan, ¾ inch up the sides.
Bake 65–80 minutes until edges are set and centre jiggles slightly.
Turn oven off. Leave cheesecake inside for 1 hour.
Remove from water bath, cool on rack for 1 hour.
Cover and refrigerate at least 24 hours.
Release ring, slice with a warm dry knife, and serve.