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Step 1
Start the day before you want to bake the bread. Place the bread flour and plain flour in the bowl of a stand mixer fitted with a dough hook. Add the yeast to one side of the bowl and the salt and sugar to the other and mix to combine.
Step 2
Add the aquafaba, milk and vanilla extract and stir to form a rough dough then place the mixer on a medium speed and knead the dough until it is smooth and elastic. You can also knead the dough by hand on an unfloured surface instead.
Step 3
Add the softened butter or olive oil and mix until it is fully combined and the dough is smooth again, it will be quite soft and sticky. I actually find it easier to mix the fat in by hand rather than with the mixer (in a bowl, not on a surface if you are using olive oil). It will take a while to fully mix it all in and it will look like it is not going to work but trust me, keep going!
Step 4
Once the fat is fully mixed in, keep kneading until the dough pulls away from the sides of the bowl cleanly, it will still be quite soft and sticky however. Place the dough in a bowl, cover it and place it in the fridge to rise overnight.
Step 5
The next day the dough should have at least doubled in size. Line a 2 - 2 1/2 lb loaf tin with baking parchment. My loaf tin measures 11.5 x 21.5 cm / 4.5 x 8.5 in. You don't want it to be any smaller than this; a 13 x 23cm / 9 x 5 in one would also be fine.
Step 6
Punch down the dough then you have a couple of options for shaping it. You can simply shape it into a loaf and place it in the lined tin; or to make a loaf as pictured that you can pull apart, divide the dough into either 6 or 8 even pieces (I prefer 8).
Step 7
Shape each piece into a smooth ball. To do this, pull the edges of the piece of dough in towards the middle and pinch them together. flip the ball over onto a lightly floured surface and cup your hand around it. Gently roll the ball on the work surface to form a smooth ball. Repeat with the rest of the dough portions.
Step 8
Arrange the balls in two rows in your loaf tin. You will probably have to squish them together to fit them in.
Step 9
Loosely cover the tin and set aside to rise until doubled in size. Because the dough is so heavily enriched this can take some time, about 1 - 2.5 hours depending on how warm it is. It is ready when it is puffy and if you gently poke it with a finger it springs back slowly. If it springs back quickly then it needs longer; and if it deflates then it is over-proved and you will need to punch it down, reshape it and let it rise again.
Step 10
When the loaf is nearly ready, preheat the oven to 180°C/350°F/gas mark 4 and prepare the glaze. Simply whisk together the milk, maple syrup and oil in a small bowl.
Step 11
When the loaf is ready, gently brush it with some of the glaze, try not to let it drip down the sides as that can cause it to stick to the tin and hinder the oven spring.
Step 12
Bake the brioche for 20 minutes then brush it with more of the glaze, turn the oven down to 160°C/320°F/gas mark 3 and bake for a further 25-30 minutes until the internal temperature reaches 94°C/201°F on a probe thermometer. If you don't have a thermometer then a skewer inserted into the centre should come out clean. If it starts to darken too much on top before it is ready then you can loosely cover it with tin foil.
Step 13
Once the loaf is ready, let it cool in the tin for 15 minutes then turn it out onto a wire rack and let it cool completely before slicing. Once cool store in an airtight container.