In a medium saucepan, whisk together the sugar, cornstarch, and salt.
Gradually add the milk while whisking until the mixture is smooth.
Place the saucepan over medium heat and cook, stirring constantly, until the mixture thickens.
Stir in the finely ground pistachios and continue cooking for another 1–2 minutes.
Remove from the heat and add the vanilla extract and heavy cream. Stir until well combined.
Pour the pudding into individual serving glasses or bowls.
Cover and refrigerate for at least 2 hours, or until completely chilled and set.
Before serving, garnish with whipped cream and chopped pistachios.