Make Tangzhong Paste:

Combine the water and bread flour in a small saucepan, whisking them together. Set over medium heat and cook, whisking continuously, until the mixture becomes a thick paste, roughly 4–5 minutes. Transfer to a small bowl and reserve for later use.

Mix Dough Ingredients:

In a stand mixer bowl equipped with the dough hook, mix the bread flour, sugar, yeast, and salt. Pour in the milk, egg, and tangzhong. Knead on low speed for 2 minutes until the dough comes together.

Knead in Butter:

While the mixer runs on low, incorporate the softened butter one tablespoon at a time, ensuring each addition is fully absorbed before adding the next. After all butter is added, raise the speed to 2 on a KitchenAid and knead for 12 minutes, or until the dough is smooth, elastic, and passes the windowpane test.

First Rise:

Form the dough into a ball and put it in a lightly greased bowl. Cover and allow it to rest at room temperature for 30–45 minutes.

Cut Parchment Squares:

While the dough rests, cut out 8–9 squares of parchment paper.

Roll and Cut Donuts:

Transfer the dough to a floured work surface, dust the top with flour, and roll it to a thickness of 3/4 inch. Using a large round donut cutter, cut out donuts (you should get about eight from dough rolled to 3/4 inch). Gently knead the leftover dough together, let it rest for 5–10 minutes, then roll and cut again.

Proof Donuts:

Set each donut on a parchment square and arrange them on a baking sheet. Loosely cover with plastic wrap and let them rise until puffy and doubled in size, about 45–65 minutes.

Heat Oil:

When the donuts are roughly halfway through their final proof, begin heating 3–4 inches of oil in a heavy pot to 350°F (175°C). Line a baking sheet with a wire rack. Monitor the temperature; if the oil reaches 350°F (175°C) before the donuts are ready, lower the heat slightly to maintain it until proofing finishes.

Fry Donuts:

In small batches, use a metal slotted spoon to carefully lower 2–3 donuts (still on their parchment) into the hot oil, then remove the paper with tongs. Fry for about 2 1/2 minutes total, flipping once halfway, until golden brown. Move to the wire rack to drain.

Prepare Glaze:

In a medium bowl, whisk the powdered sugar, hot water, vanilla, and salt until smooth. Adjust the consistency with more water or powdered sugar to achieve a thick yet pourable glaze.

Glaze Donuts:

Dip each donut on both sides into the glaze, allowing excess to drip off, then return them to the wire rack over the baking sheet.

Set and Serve:

Let the donuts sit for about 45–60 minutes until the glaze sets completely, then serve and enjoy!