Prepare Tangzhong: In a saucepan, combine bread flour and milk. Cook over medium heat, stirring constantly until thick, about 2-3 minutes. Let it cool completely.

Dough Preparation: In a large bowl, combine tangzhong, sourdough starter, eggs, sugar, and bread flour. Mix until homogeneous and let rest for 30 minutes.

Knead Dough: Sprinkle in salt and knead for about 10 minutes. Gradually add softened butter until fully incorporated and shiny.

Bulk Fermentation: Transfer dough to a greased bowl, cover, and let rise in a warm area until nearly doubled in size (about 4 hours).

Shape Donuts: Roll out dough to 1/2 inch thickness and cut out shapes. Place on a lined baking sheet, allowing to proof until puffy (3-4 hours).

Fry Donuts: Heat oil to 360°F. Fry donuts until golden brown (about 2 minutes each side). Remove and drain on paper towels.

Cool & Glaze: Prepare glazes by mixing powdered sugar with milk and vanilla, or adding cocoa for chocolate. Dip donuts and let set before serving.