Preheat oven to 325 degrees. Line standard muffin tins with paper liners. Stir together crackers, butter, and 3 tablespoons sugar; press 1 tablespoon into bottom of each cup. Bake until set and beginning to color at edges, about 10 minutes. Transfer tins to rack to cool.
Puree raspberries in a food processor until smooth, about 30 seconds. Press through a fine sieve; discard solids. Whisk in 2 tablespoons sugar.
With mixer on medium-high, beat cream cheese until fluffy. On low, add remaining 1 1/2 cups sugar in a slow stream. Mix in salt and vanilla until well combined. Add eggs, one at a time, beating until just combined after each (do not overmix) and scraping bowl.
Spoon 3 tablespoons filling over crust in each cup. Drop two dots of raspberry puree about 1 inch apart in cupcake. Drag the tip of a toothpick or wooden skewer down through centers of dots to create a heart.
To bake, set tins in oven in roasting pans filled halfway with hot water; bake until set, about 34 minutes, rotating halfway through. Transfer tins to racks to cool completely. Refrigerate in tins, uncovered, at least 4 hours; remove from tins.
Refrigerate in air-tight containers up to 5 days.
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