Start by preparing the dough. In a large mixer bowl, combine the flour, sugar, yeast, salt, and cinnamon or pumpkin spice if you're using it. Add the pumpkin purée, oil, and water to the dry ingredients, start the mixer on low, and knead for 10-15 minutes until you have a soft, smooth dough. Place it in a greased bowl. Cover with a clean towel and let it rise in a warm place for about an hour, or until it has doubled in size.
Once the dough has risen, punch it down to release the air. Divide it into 8 to 10 equal portions and shape each portion into a round bun.
Optional: Cover the buns with a towel, then take one out. Flatten it with a rolling pin until it’s about ⅓ inch thick, then roll it tightly into a log. Extend the log by rolling it further, and twist it into a spiral shape.
Place the buns on a parchment-lined baking sheet, leaving space between each for rising. Cover again with a towel and let them rise for another 30 to 45 minutes.
While the buns are rising, preheat your oven to 350°F (175°C) and prepare the vegan “egg wash.” In a small bowl, whisk together the maple syrup and plant milk. Once the buns have risen, brush the tops with the “egg wash” mixture to give them a golden, shiny finish when baked.
Bake the buns for about 25 minutes, or until they are golden brown. Let them cool slightly before serving.