In a small saucepan, heat the coconut milk until it's just barely simmering over medium heat. Remove from the heat and whisk in the pumpkin purée until smooth.
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‐pumpkin 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, 5–8 minutes (if you are kneading by hand it will take a little longer). Then slowly add the butter by the tablespoon, letting each tablespoon fully incorporate into the dough before adding the next.
Once the butter has been fully incorporated, test the dough. If you press a floured finger lightly onto it, it should spring back slowly (if not, continue kneading and re‐test in a few more minutes). The dough should be tacky but not crazy sticky, if it feels way too wet & sticky, add another tbsp or 2 of flour until it is a little drier.
With lightly floured hands, transfer the dough 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).