Activate the yeast. Warm the almond milk in the microwave for 35–40 seconds. It should be warm, but not hot, or it can kill the yeast. Pour it into the bowl of an electric stand mixer, add the cane sugar, and sprinkle the yeast on top. Stir briefly and let it sit for 10 minutes, until foamy.
Add the wet ingredients. Stir in the pumpkin puree and melted vegan butter with a spatula until combined.
Add the dry ingredients. Add 3 3/4 cups of the flour, along with the salt and pumpkin pie spice. Stir with a spatula until a dough begins to form.
Knead. Attach the dough hook and knead on low speed for 7–8 minutes. If the dough looks wet and is sticking to the sides of the bowl after a few minutes, add more flour 1 tablespoon at a time. The finished dough should form a springy ball that's only slightly sticky.
First rise. Transfer the dough to a lightly greased large bowl (the mixing bowl works fine), cover with a towel, and let rise in a warm place for 1 hour, or until doubled in size. Placing the bowl in the oven with just the light on creates a nice warm spot.