In a small saucepan, bring the coconut milk just to a simmer over medium heat (don't let it bubble too much). Remove from the heat and add the coconut oil / vegan butter to the saucepan to melt. Once melted, add the milk mixture to a small bowl and let it cool until it's just warm to the touch (not hot, or it will kill the yeast), about 40 degrees celsius / 105 fahrenheit. Once the mixture has cooled, add the sweet potato purée and whisk to combine.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with a wooden spoon, combine the flours, sugar, yeast, and salt. Add the milk‐sweet potato mixture and mix just until combined.
Switch to the dough hook and knead the dough on low speed until it begins to come together, then increase the speed to medium‐high and knead until the dough is smooth and elastic and pulls away from the side of the bowl, about 8–10 minutes (if you are kneading by hand it will take a little longer). If you press a floured finger lightly onto the dough, it should spring back slowly (if not, continue kneading and re‐test in a few more minutes). The dough should be lightly tacky but not too sticky, if it feels too wet & sticky, add another Tbsp or 2 of flour until it is a little drier.
Form the dough into a ball and transfer it to a lightly oiled bowl, cover it, and leave it in a warm, draft‐free spot until it has doubled in size, about 1 to 2 hours (depending on the temperature of the room and activity of the yeast).