In a medium saucepan, combine the milk and heavy cream over medium heat. Stir occasionally until the mixture is hot but not boiling. Remove from heat.
In a separate bowl, whisk together the sugar, cornstarch, and salt. Add the egg yolks and whisk until smooth.
Gradually pour the hot milk mixture into the egg yolk mixture, whisking constantly to temper the eggs.
Return the mixture to the saucepan and cook over medium heat, stirring constantly until it thickens and begins to bubble, about 5-7 minutes.
Remove from heat and stir in the vanilla extract and pistachio paste until well combined.
Transfer the pistachio cream to a bowl, cover with plastic wrap directly on the surface to prevent a skin from forming, and refrigerate for at least 2 hours or until chilled.
Once chilled, stir the cream gently before serving. Spoon into dessert cups and top with chopped pistachios for garnish.