Whisk together the sugar, cornstarch and salt in a large saucepan; whisk in the milk until smooth. Heat over medium-high heat, whisking, until bubbles begin to form. Remove from the heat.
Whisk the egg in a medium bowl. Slowly pour 1/4 cup of the hot milk mixture into the egg while whisking vigorously until smooth. Pour the mixture back into the saucepan and cook over medium-high heat, whisking vigorously, until thick and starting to bubble, about 2 minutes. Transfer the mixture to a bowl and let cool until thick, whisking frequently. Whisk in the sour cream and vanilla.
Scoop about 1 scant tablespoon vanilla pudding into each tartlet shell and top each with a raspberry. Serve immediately, or cover and refrigerate up to 2 hours.