In a large mixing bowl, whisk together the flours, sugar, and salt. Add in the vegan butter and use your hands to "cut" the fat into the flour. You should end up with a sandy texture.
Once you have a sandy texture, add in the sourdough starter and water. Stir until a dough forms. Once the dough comes together, cover the mixing bowl with plastic or a damp tea towel and let the dough rest for 30 minutes.
After 30 minutes, knead the dough, either with your hands or a stand mixer fitted with the dough hook, for about 7 to 8 minutes. The dough should be smooth and supple.
Place the dough back into the mixing bowl and cover it with plastic or a damp towel. Allow it to bulk rise for 10 to 12 hours at room temperature or until doubled in size. Or place the dough in a warm place, about 80℉ for 3 to 4 hours or until the dough has doubled in size.
After the bulk rise, dump the dough onto a lightly floured surface. Press it into a rectangle and then form it into a loaf. Place it in a greased loaf pan and cover it with a plastic bag for its second rise, this is for an hour. You want it to rise until it is close to or a little above the edge of the loaf pan.
Halfway through the rising process, preheat your oven to 500°F. Once the bread has fully risen and you're ready to bake it, reduce the oven temperature to 375°F and bake the bread for 45 to 50 minutes.
Remove the loaf from the oven and allow it to cool for 10 minutes in the pan before removing it to a wire rack to cool completely.
Store in a bread bag on the counter for up to a week or slice and freeze for up to 3 months