Boil the cubes of potato in water for about 8 to 10 minutes until soft. Pass the boiled potato through a ricer or grate finely on a box grater.
Heat milk to 110°F to 130°F in a bowl in the microwave or over the stove top in a small sauce pan.
In the bowl of a stand mixer with the dough hook add 3 ½ cups bread flour, sugar, quick rise yeast, nutmeg, and sea salt and stir over low to combine. Then add riced or grated potato, unsweetened apple sauce, vegan butter, and combine over low speed, while adding the warm milk. Continue mixing until it comes together to form a sticky ball around the hook. If the dough looks too wet, add a little bit of bread flour 1 tablespoon at a time until the dough is soft and slightly sticky. Coat the ball of dough with vegetable oil. Cover the bowl with a dish towel or plastic wrap and let it rise in a warm spot until doubled in size, about 40 minutes to 1 hour.
To make the filling in a medium bowl combine softened vegan butter, miso, brown sugar and cinnamon until it’s a smooth paste and set aside.
To make the miso caramel pan sauce, in a medium microwave safe bowl, add vegan butter, miso, maple syrup, brown sugar, and cinnamon. Microwave for 30 seconds until the butter is slightly melted and you can stir everything together into a sauce. Scoop 1 tablespoon + 1 teaspoon of miso caramel pan sauce into each cup of a 12 cup muffin pan. You can also use a rectangular baking dish instead of a muffin pan and pour all the caramel into the bottom.
Once the dough is doubled in size, turn it out on a lightly floured surface and roll out the dough into an 18 x 12-inch rectangle. Brush the filling all over the dough. Starting on the shorter end of the dough, roll up the dough from end to end to form a cylinder. Use a dough cutter or sharp knife to cut 12 even 1-inch pieces. Place one piece in each muffin cup or in rows in the baking dish, slightly spaced apart. Cover and let it rise for 30 minutes until puffy. Preheat the oven to 350°F towards the end of the rising time. Bake for 18 to 20 minutes.
Once baked, let cool for 10 minutes in the tray and using oven mitts, invert the muffin pan onto a large board or baking pan. Let the caramel pan sauce drip down over the buns and scoop any extra caramel onto the sticky buns, if necessary. If you used a square baking dish you can serve right from the dish or invert the pan onto a board or baking sheet to show the caramel on top.