In a heat-proof container, whisk together the oat milk, olive oil, sugar, and aquafaba. Place it in the microwave for about 30 seconds. You want it to be warm, but not hot, just a little over room temperature, like between 80-90 degrees.
Place the warmed mixture into the bowl of your stand mixer and sprinkle the yeast over it. Leave for 5-10 minutes to bloom.
Add the flour and salt, and, using the dough hook attachment, begin to mix. Leave it to mix for about 10 minutes until the dough is smooth.
Form into a ball, drizzle a little extra olive oil over and rub it all over the ball. Place the ball back in the bowl, cover, and allow to rise somewhere warm for about an hour.
After the first rise is complete, punch it down and then place in the fridge to do a second, cold rise. This should go for four hours, or overnight.
Remove the dough from the fridge and place on your work surface. Divide in half and then divide each half into 3 to make 6 dough balls. Work with 2 at a time.
Roll the balls out into rectangles, as thin as you can get them. Then brush each rectangle with melted vegan butter, and sprinkle over an even, thin layer of cinnamon, brown sugar and cardamom. Starting at the long edge, roll it up into a roll as tightly as you can and pinch the seam shut. Now using a sharp knife, cut down through the middle of the roll lengthwise. You want to try to get all the way through the outer layers to the centre of the roll. "Butterfly" it flat open. Now take both split rolls and attach them together at the top. Weave one over the other to create the "braid," then pinch together again at the bottom to fasten. Place in a greased loaf pan and cover and allow to rise one last time, about an hour or two.
When you’re almost ready to bake, preheat the oven to 375°F, and bake for about 25 minutes, until golden.
Sprinkle with powdered sugar to serve.