01 - Combine flour, sugar, yeast, and salt in a large mixing bowl. Pour in lukewarm milk, add softened butter and egg. Mix until shaggy dough forms, then knead by hand or stand mixer for 8–10 minutes until smooth and elastic. Cover bowl with plastic wrap and place in warm draft-free area for 1 hour until doubled in volume.
02 - Place raspberries, sugar, and lemon juice in small saucepan. Simmer over medium heat, stirring occasionally, for 7–8 minutes until mixture thickens to jam-like consistency. Remove from heat and allow to cool completely before using.
03 - Beat cream cheese, icing sugar, rose water, and egg yolk in medium bowl until completely smooth and creamy. Refrigerate until ready to assemble buns.
04 - Punch down risen dough to release air. Divide into 12 equal portions. Flatten each piece into 4-inch disc and arrange on parchment-lined baking sheet, spacing 2 inches apart.
05 - Press deep indentation into center of each disc using thumb or spoon handle. Spoon 1–2 teaspoons cheesecake filling into each hollow, then top with 1 teaspoon cooled raspberry compote. Cover loosely with clean kitchen towel and let rise 30–40 minutes until puffy and visibly increased in size.
06 - Preheat oven to 350°F. Brush exposed dough edges with milk using pastry brush. Sprinkle with demerara sugar if desired. Bake for 20–25 minutes until golden brown and tops feel set when lightly touched. Cool on baking sheet for 10 minutes before garnishing.
07 - Sprinkle warm buns with chopped pistachios or dried rose petals if using. Serve warm or at room temperature.