Mix the Dough Add lukewarm milk, egg, sugar, salt, and instant yeast to the mixer bowl and stir to combine. Add melted, cooled butter and bread flour. Mix at a low setting until no dry flour remains, then increase speed and knead until smooth, elastic, and able to pass a thin windowpane test.

Let the Dough Rise Transfer dough to a lightly greased container. Proof in a folding proofer at 26–28°C / 79–82°F for ~1½ hours until approximately doubled.

Prepare the Butter Filling Cut 80 g salted butter into eight 10 g pieces and refrigerate until needed.

Make the Cinnamon Topping Beat softened butter and sugar until smooth. Gradually mix in 45 g beaten egg. Stir in ground cinnamon and cooled water (from the step-by-step description). Add all-purpose flour and mix just until smooth. Transfer to a piping bag.

Divide and Rest Gently press risen dough to release gas. Weigh and divide into 8 equal portions (~74 g each). Round each portion into a ball, cover, and rest for 10 minutes.

Fill and Shape Flatten each ball into a small disk. Place one cold butter piece in the center, bring dough around it, and pinch seams firmly closed. Place seam-side down on parchment-lined baking trays.

Proof the Buns Proof in the proofer at 26–27°C / 79–81°F for ~1 hour (keeping setting below 28°C / 82°F) until airy and nearly doubled.

Pipe and Bake Preheat oven to 180°C / 350°F. Snip piping bag opening and pipe a tight spiral over the top two-thirds of each bun dome. Bake for 20–24 minutes until the topping is set and crisp and exposed bread is golden. Cool briefly on tray before moving to a wire rack. Serve warm.