To make the tangzhong: Combine all of the tangzhong ingredients in a small saucepan, and whisk until no lumps remain., Place the saucepan over low heat, and cook the mixture, whisking constantly, until thick and the whisk leaves lines on the bottom of the pan, about 3 to 5 minutes.

, Transfer the tangzhong to a small bowl and let it cool to room temperature., To make the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Combine the flour with the tangzhong and the remaining dough ingredients, then mix and knead — by hand, mixer, or bread machine — until a smooth, elastic dough forms.

, Shape the dough into a ball, and let it rest in a lightly greased covered bowl until puffy but not necessarily doubled in bulk, about 60 to 90 minutes.

, To shape the doughnuts: Deflate the dough and turn it out onto a lightly floured surface. Gently roll it ¼" thick, and cut out doughnuts with a 2 ½" to 3" round cutter., Cover loosely with greased plastic wrap and let the doughnuts rise for 30 minutes to an hour, until doubled in size., To fry: Heat the oil or shortening in a heavy frying pan or skillet to 350°F. Carefully place the doughnuts in the oil, two or three at a time, and fry until golden brown. Turn over and cook the second side; each side should take no more than a minute., Remove the doughnuts from the oil with a slotted spoon and drain on absorbent paper. Repeat with the remaining dough., Frost the doughnuts as desired, using your choice of sugar topping or glaze., Storage information: Doughnuts are best eaten the day they're made, ideally served still warm. Store leftovers, unfrosted and unfilled, in an airtight container at room temperature for up to two days; freeze for longer storage.