01 - In a large mixing bowl, combine flour, caster sugar, instant yeast, and salt. Pour in lukewarm milk, add softened butter, and crack in the egg. Mix ingredients until a shaggy, rough dough forms. Transfer to a lightly floured surface and knead by hand for 8 to 10 minutes, or use a stand mixer with dough hook, until smooth, elastic, and slightly tacky. Cover bowl with plastic wrap and place in a warm, draft-free area for 1 hour or until dough has doubled in size.
02 - Place raspberries, caster sugar, and lemon juice in a small saucepan. Set over medium heat and bring to a gentle simmer. Cook for 7 to 8 minutes, stirring occasionally, until raspberries break down and mixture thickens to a jam-like consistency. Remove from heat and allow to cool completely at room temperature before using.
03 - In a medium bowl, beat room temperature cream cheese with icing sugar until smooth and creamy. Add rose water and egg yolk, continuing to beat until fully incorporated and no lumps remain. Set aside at room temperature until ready to assemble.
04 - Punch down the risen dough to release air pockets. Turn onto a lightly floured surface and divide into 12 equal portions, approximately 2 ½ oz each. Working with one piece at a time, flatten each portion into a 4-inch round disc. Arrange discs on a parchment-lined baking sheet, leaving 2 inches of space between each for expansion.
05 - Using your thumb or the back of a spoon, create a deep indentation in the center of each dough disc, leaving a ½-inch border around the edges. Spoon 1 to 2 teaspoons of cheesecake filling into each indentation, then top with 1 teaspoon of cooled raspberry compote. Avoid overfilling to prevent leakage during baking.
06 - Loosely cover the baking tray with a clean kitchen towel or plastic wrap. Place in a warm area for 30 to 40 minutes until buns appear puffy and have increased noticeably in size. The dough should spring back slowly when lightly pressed.
07 - Preheat oven to 350°F. Using a pastry brush, lightly coat the exposed dough edges of each bun with milk. If desired, sprinkle demerara sugar over the dough edges for a crunchy, sparkling finish.
08 - Place baking tray in preheated oven and bake for 20 to 25 minutes. Rotate tray halfway through baking for even browning. Buns are done when tops are golden brown and filling is set. Remove from oven and allow to cool on baking sheet for 10 minutes before transferring to a wire rack. Garnish with chopped pistachios or dried rose petals while slightly warm, if desired.