1. Preheat oven to 325 degrees. Place paper liners in the cups of two standard 12-cup muffin tins, and set aside.

2. Stir together cracker crumbs, melted butter, and 2 tablespoons sugar in a medium bowl. Press 1 tablespoon of the crumb mixture firmly onto bottom of each cup in muffin tin. Bake until set, about 5 minutes. Let cool in tins on a wire rack. Leave oven on.

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 4 1/2 teaspoons sugar, and set aside.

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). Spoon 3 tablespoons filling into each cup.

5. Drop raspberry sauce by the 1/2 teaspoon over cakes. With a wooden skewer or toothpick, swirl sauce into filling.

6. Bake until set, 10 to 12 minutes. Let cool completely in tins on a wire rack. Refrigerate, uncovered, 1 hour or overnight.