Preheat oven to 350°F. Wrap exterior of a 9-inch springform pan (including base) in a double layer of foil; set aside.
Stir together cracker crumbs, melted butter, and 2 tablespoons sugar in a medium bowl.
Press crumb mixture firmly onto bottom of pan. Use the bottom of a measuring cup or the flat side of a drinking glass to press the crumbs into a compact layer.
Bake until set, about 10 minutes. Let cool in pan on a wire rack. Reduce oven temperature to 325°F.
Put cream cheese in the bowl of an electric mixer fitted with the paddle attachment; mix on medium speed until fluffy, about 3 minutes.
With mixer on low speed, add sugar in a slow, steady stream. Add salt and vanilla; mix until well combined.
Add eggs, one at a time, mixing each until just combined (do not overmix).
Pour cream cheese filling over crust.
Set cake pan inside a large, shallow roasting pan. Transfer to oven. Carefully ladle boiling water into roasting pan to reach halfway up sides of cake pan. Bake until cake is set but still slightly wobbly in center, 60 to 65 minutes.
Transfer cake pan to rack; let cake cool completely. Refrigerate, uncovered, 6 hours or overnight. Before unmolding, run a knife around edge of cake.
