To make the tangzhong, place the flour in a saucepan and gradually whisk in the milk to avoid lumps.
Place the pan over a medium/low heat and whisk constantly until the mixture has thickened to a paste/pudding-like consistency.
Scrape the tangzhong into the bowl of a stand mixer fitted with a dough hook and pour the rest of the cold milk on top. This will cool the tangzhong down so that the heat doesn’t kill the yeast.
Add the sugar, salt and flour and finally the yeast. Stir until it forms a rough dough then set the stand mixer to a medium speed and mix until the dough is smooth and stretchy, this can take about 10 minutes.
Add the vegan butter and knead for about another 5 minutes until it is fully incorporated and the dough is smooth, elastic and no longer feels greasy. You may need to scrape down the sides of the bowl a couple of times.
You should be able to stretch a section of the dough thin enough to see light through it without it breaking (the windowpane test). If it seems too wet then you can knead in a little extra flour, a tablespoon at a time. Be careful though, this is meant to be a very soft, sticky dough and adding too much extra flour will make the bread dry.
Place the dough in a lightly oiled bowl, cover and place in the fridge to rise overnight, or in a warm spot for 1-2 hours, until doubled in size.
The following day (or once the dough has doubled in size at room temperature), knock back the dough and give it a brief 30 second knead to knock out the air bubbles. Line a 23 cm/9 in square tin with baking parchment.
Divide the dough into 9 or 12 even pieces and shape each one into a ball. You can either arrange them in the tin now, or follow the shaping instructions below for rolls shaped like the ones in the photos.
Roll each ball out into a long oval, fold one third of the oval over the middle (from the side, not the top), then the other third over the top to form a long, narrow packet.
Roll over the seam to flatten it, then roll it up tightly from one end to make a fat sausage. Repeat with the other balls of dough then arrange them in the tin, seam side down.
Loosely cover and leave to rise until puffy, about 45-60 minutes. If you gently press the dough with your finger it should spring back slowly, and maybe leave a slight indentation. If it springs back quickly then it needs a little longer, and if the dough deflates then it is over-prooved so keep an eye on it!
When the bread is nearly ready, preheat the oven to 180°C/160°C fan/350°F/gas mark 4.
Gently brush any exposed dough with a little milk, then bake the rolls for 30 minutes. They should be deep golden and a probe thermometer inserted into the centre should reach at least 90°C/194°F.*
Allow to cool in the tin for 10 minutes then carefully lift it out onto a wire rack and leave to cool for about 30 minutes before serving.