In a stand mixer using the dough hook, or in a large bowl with a wooden spoon, combine the flour, yeast and salt. Add the milk mixture, egg and mashed potatoes. Knead vigorously until the dough begins to form.
Gradually add the butter and oil. In the stand mixer or by hand, knead for about 5 minutes until the dough is smooth and slightly sticky. Place in a clean, lightly oiled bowl. Cover with a damp cloth and let rise in a warm, humid place for about 30 minutes or until the dough has doubled in volume.
Butter an 8-inch (20 cm) springform pan and line the bottom with parchment paper.
In a small bowl, combine the brown sugar and cinnamon. Set aside.
On a floured surface, roll out the dough into a 24 x 6-inch (60 x 15 cm) rectangle. Brush with the melted butter, and spread the brown sugar mixture over the surface of the dough. Cut the dough lengthwise into three 24 x 2-inch (60 x 5 cm) strips.
Loosely roll a strip of dough onto itself and around the handle of a wooden spoon. With another strip, continue spiralling the dough around the wooden spoon. Repeat with the last strip. Place the rolled dough into the centre of the prepared pan and remove the spoon. Do not cover. Let rise in a warm, humid place for about 1 hour and 30 minutes or until the dough has risen over the top of the pan.
With the rack in the middle position, preheat the oven to 350°F (180°C).
Brush the dough with milk. Bake for 30 minutes or until golden brown. Let cool. Unmould.
In a bowl, combine the icing sugar and milk. When ready to serve, glaze the cinnamon roll cake.