Preparation
Rub the T55 flour, salt, and butter (1) together in a mixing bowl fitted with a paddle attachment until a sandy texture is achieved. Incorporate the water and vinegar, then continue to mix until a rough dough is formed. Roll the dough into a 20 cm × 20 cm square. Store in the chiller for 4 hours. Briefly mix butter (2) and T45 flour together in a mixing bowl fitted with a paddle attachment. Roll the butter mixture into a 20 cm × 40 cm rectangle. Store in the chiller for 4 hours.
Steam-bake the taro at 100 °C for 45 minutes. Combine cooked taro, caster sugar, trehalose, butter, and purple sweet potato powder in a mixing bowl fitted with a paddle attachment and mix until a smooth paste is formed.
Assembly
Place the Détrempe on top of the Beurre-Manié, and stack it with another piece of Détrempe. Give the dough a double fold (rolling it to thickness setting No. 5). Rest the dough for 4 hours in the chiller. Give it another double fold (rolling to No. 5). Rest the dough for 4 hours in the chiller. Give it a book fold (rolling to No. 6). Rest the dough for 4 hours in the chiller. Roll the width of the dough to 30 cm, then rest it for 2 hours in the chiller. Roll the dough to a thickness of 3.5 mm and rest for 2 hours in the chiller. Roll to a final thickness of 3 mm.