In a medium mixing bowl, whisk bread flour with milk until completely smooth. Transfer to a small skillet and cook over medium heat, stirring constantly with a rubber spatula, until it slightly thickens into a smooth paste. NOTE: Do not overcook — it should look like a loose pudding, not dry. Scrape back into the same bowl and let cool for 5 minutes.

To the cooled base, add milk and egg. Whisk until smooth. Add bread flour, sugar, yeast, and salt. Mix with a stiff spatula or dough hook until a sticky dough forms. NOTE: It won’t look shaggy — more like a wet, cohesive blob.

Knead in the bowl for 1–2 minutes, then transfer to a clean, unfloured surface. Use slap-and-fold or stretch-and-fold motions. NOTE: The dough will be sticky — resist the urge to add flour. Knead 3–5 minutes until the dough begins to tighten and feel slightly elastic.

Add softened unsalted butter. NOTE: It may feel greasy or fall apart — keep kneading until the dough becomes smooth and elastic (6–8 minutes).

Form the dough into a ball and return it to the bowl. Cover and let rise at room temp (around 72°F) for 60–90 minutes until doubled in size. NOTE: In warmer kitchens (78°F or more), start checking around 45–60 minutes.

Turn the dough onto a lightly floured surface. Divide into equal pieces. Full-size buns: Divide into 4 (about 105g each). Slider buns: Divide into 9 (about 50g each). Shape each piece into a taut ball using tension pulls. Gently flatten each one slightly and transfer to a parchment-lined sheet pan.

Cover loosely and let rise 45–60 minutes at room temperature until puffy and domed.

Preheat oven to 375°F. In a small bowl, whisk together egg yolk and milk. Brush tops of the buns gently. Optionally, sprinkle with sesame seeds. Bake until deeply golden brown. Full-size buns: 14–16 minutes. Slider buns: 12-14 minutes.

Transfer buns to a wire rack and cool for at least 20 minutes before slicing or serving.