Make the Tangzhong: In a small saucepan, whisk together the 50g milk, 50g water, and 20g bread flour. Cook over medium heat, stirring constantly, until the mixture thickens to a paste-like consistency, about 2-3 minutes. Remove from heat and let cool completely.

In a large bowl, combine the 110g all-purpose flour, 250g bread flour, and 10g fresh or instant yeast. Create a well in the center and add the 100g warm milk, 1 whole egg, 2 egg yolks, 1 tsp vanilla, 60g sugar, and 1 tsp salt. Mix until a shaggy dough forms.

Turn the dough out onto a lightly floured surface and knead for about 10 minutes, until smooth and elastic. Add the 50g soft butter and knead for an additional 5 minutes, until the butter is fully incorporated.

Place the dough in a lightly greased bowl, cover, and let rise for 1 hour, or until doubled in size.

Punch down the dough to release any air bubbles. On a lightly floured surface, roll the dough into a rectangle about ½-inch thick. Sprinkle the 150g French Pearl sugar evenly over the dough.

Tightly roll the dough into a log, starting from the short side. Pinch the seam to seal. Cut the log into 8 equal pieces.

Place the pieces, cut-side up, in a greased 9-inch round baking pan. Cover and let rise for 30 minutes.

Preheat the oven to 375°F (190°C).

In a small bowl, whisk together the 1 egg yolk and 1 tbsp milk for the egg wash. Brush the tops of the dough pieces with the egg wash.

Bake for 25-30 minutes, until golden brown. Immediately sprinkle with the 1 tsp caster sugar.

Serve warm.