Step 1

Preheat oven to 350 degrees. Wrap exterior of a 9-inch springform pan (including base) in a double layer of foil; set aside.

Step 2

Stir together cracker crumbs, melted butter, and 2 tablespoons sugar in a medium bowl. Press crumb mixture firmly onto bottom of pan. Bake until set, about 10 minutes. Let cool in pan on a wire rack. Reduce oven temperature to 325 degrees.

Step 3

Process raspberries in a food processor until smooth, about 30 seconds. Pass puree through a fine sieve into a small bowl; discard solids. Whisk in 2 tablespoons sugar, and set aside.

Step 4

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 remaining 1 1/2 cups 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.

Step 5

Drop raspberry sauce by the teaspoon on top. With a wooden skewer or toothpick, swirl sauce into filling.

Step 6

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.

Step 7

Transfer cake pan to rack; let cake cool completely. Refrigerate, uncovered, 6 hours or overnight. Before unmolding, run a knife around edge of cake.