01 - Combine flour, sugar, yeast, and salt in a large mixing bowl. Pour in lukewarm milk, add softened butter and whole egg. Mix until shaggy dough forms, then knead by hand or stand mixer for 8-10 minutes until smooth and elastic. Cover bowl with damp towel and set in warm place for 1 hour until doubled in volume.
02 - Place raspberries, caster sugar, and lemon juice in small saucepan. Cook 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 room temperature cream cheese, icing sugar, rose water, and egg yolk in medium bowl until completely smooth and creamy. Set aside until ready to fill buns.
04 - Punch down risen dough to release air. Divide into 12 equal portions and roll into balls. Flatten each ball into 3-inch disc and arrange on parchment-lined baking sheet. Press deep indentation in center using thumb or back of spoon. Fill each well with 1-2 tsp cheesecake mixture, then top with 1 tsp cooled raspberry compote.
05 - Cover baking sheet loosely with plastic wrap. Let buns rise 30-40 minutes until visibly puffy. Preheat oven to 350°F. Brush dough edges with milk and sprinkle with demerara sugar. Bake 20-25 minutes until golden brown. Cool 10 minutes before garnishing with pistachios or rose petals.