In a small bowl, add the water, yeast, a tablespoon of sugar and a tablespoon of flour, give it a stir, and let it sit for 10 minutes until the yeast forms a bubbly foam.
In a large bowl, sift the flour, and add the butter. Use your fingertips to rub the butter until the flour ressembles breadcrumbs.
Add the egg, sugar, pumpkin pie spice and pumpkin puree.
Once the yeast is foamy, add it to the bowl and knead everything together for at least 5 minutes until you get an elastic dough that does not stick to the bowl.
Cover with clingfilm and a clean tea towel, and let it sit for at least one hour or until it doubles its size.
To make the filling, mix the pumpkin puree with the sugar and cinnamon.
Use a rolling pin to roll out the dough into a rectangle, spread the pumpkin all over, then roll the dough into a big sausage.
Line a baking tray with non-stick paper, cut 12 pinwheels out of the big roll, and arrange on the tray, leaving a bit of space between each roll.
Cover with clingfilm, and let it sit again for 30 minutes to one hour, until the rolls rise and fill the space between them.
Preheat the oven to 170 degrees Celsius (340 Fahrenheit).
Bake the rolls for about 20-25 minutes or until golden and fluffy. Leave to cool for 5 minutes.
To make the glaze, sift the icing sugar, add the milk to it, and mix well to get a smooth runny paste.
Drizzle it over the rolls.