To make the tangzhong, place the flour in a saucepan and gradually whisk in the water 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 cold milk on top. This will cool the tangzhong down so that it doesn't kill the yeast.
Add the sugar, salt, wholemeal and and white flours 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 softened 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.
The dough should still be soft and sticky, but it should pull away from the sides of the bowl cleanly. 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 soft dough and adding too much extra flour will make the bread dry.
If you don't have a stand mixer then you can knead the dough by hand on an un-floured work surface but be prepared to get sticky.
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.
Once the dough has risen, punch it down and give it a brief 30 second knead to knock out the air, let it rest for 10 minutes then roll it out on a lightly floured surface into a rectangle about 20 x 38 cm / 8 x 15 in.
Starting at one of the short edges, roll the dough up tightly into a log. It should be about 20 cm / 8 in long.
Lightly grease an 11.5 x 21.5 to 13 x 23 cm / 8.5 x 4.5 to 9 x 5 in loaf tin and place the log in the tin, seam side down.
Loosely cover the tin and set aside to rise in a warm spot until the dough has risen above the top of the tin by about 2.5 cm/1 in.
If you gently press it with a finger it should spring back slowly and maybe leave a small indentation. If it springs back quickly it needs to rise for a bit longer. It should take around 45 minutes to 2 hours depending on whether the dough was refrigerated or not.
When the dough is nearly ready, preheat the oven to 200°C/180°C fan/400°F/gas mark 6.
Gently brush the top of the loaf with milk, try not to let it drip down the sides or it may stick to the tin.
Bake for about 40 minutes until it is deep brown and a probe thermometer inserted into the centre reaches at least 90°C/194°F. If you don't have a thermometer then the loaf should sound hollow if you tap it on the bottom.
Transfer the loaf to a wire rack and leave it to cool completely before slicing.