In a mixing bowl, combine the warm milk, 1 teaspoon of sugar, and the yeast. Let sit for about 10 minutes until foamy.
Whisk in the remaining sugar, the egg, and the melted butter until smooth.
Add the flour and salt, then stir until a shaggy dough forms. Turn onto a lightly floured surface and knead for 5–7 minutes, until smooth and elastic.
Place the dough in a lightly greased bowl, cover, and let rise in a warm spot until doubled in size, about 1 hour.
For the filling, mix the pistachio cream, brown sugar, cinnamon, vanilla, and salt in a small bowl until thick and spreadable. Stir in the chopped pistachios.
Grease a small baking dish (20 cm round or 20 x 20 cm square). Punch down the risen dough and roll it into a 30 x 20 cm rectangle on a floured surface.
Spread the pistachio filling evenly over the dough, leaving a small border on one long side. Roll up tightly from the opposite long edge to form a log.
Slice the log into 6 even pieces and arrange them in the prepared pan with a little space between each roll.
Pour the heavy cream around and between the rolls. Cover and let rise again until puffy, 30–40 minutes, while you preheat the oven to 180°C.
Bake for 20–25 minutes, or until the rolls are lightly golden and the centers are set.
For the icing, beat together the cream cheese and pistachio cream until smooth. Add the powdered sugar and a pinch of salt, then thin with milk until you reach a pourable consistency.
Spread or drizzle the pistachio icing over the warm rolls, sprinkle with extra chopped pistachios if desired, and serve.