In the bowl of a stand mixer fitted with the dough hook, combine the flour, yeast, and sugar. With the mixer on low, add the milk and egg and knead for 3 minutes, until just combined. Add the butter and salt, increase speed to medium, and knead for 10 minutes more, until the dough is smooth, elastic, and slightly tacky.

Transfer the dough to a lightly greased bowl. Cover and let rise at room temperature until doubled, 1 to 1½ hours, or refrigerate overnight.

Prepare the filling: In a stand mixer fitted with the paddle attachment (or using a hand mixer), beat the butter, ground nuts, and powdered sugar on medium speed until light and creamy, about 2 minutes. Beat in the pistachio paste, then slowly mix in the melted white chocolate until smooth. Chill for 10 to 15 minutes, until thickened but spreadable.

On a well-floured surface, roll the dough into a large rectangle about 16 by 12 inches (40 by 30 centimeters). Spread the filling evenly over the surface, then fold the dough in half lengthwise to enclose the filling. Roll the folded dough again to about ½ inch/1.25 centimeters thick.

Using a sharp knife or dough cutter, slice the dough into 16 even strips. Roll each strip into a spiral and place, spiral-side up, in a greased or parchment-lined 9-by-13-inch/23-by-33 centimeter pan, spaced slightly apart. Cover and let rise again until puffy and nearly doubled, 45 to 60 minutes.

Heat the oven to 340°F/170°C (static, not convection).

Bake the buns for 25 to 30 minutes, until golden brown and fully set in the center.

In a small saucepan, bring the sugar and water to a boil over medium heat. Remove from heat once the sugar is fully dissolved.

Brush the hot buns generously with syrup immediately after baking. Let cool in the pan for 10 minutes before transferring to a rack.

Melt the white chocolate in 30-second intervals in the microwave until smooth. Stir in the pistachio paste. Drizzle over the cooled buns and sprinkle with ground pistachios before serving.