Make the dough: To a mixing a stand mixer bowl add the flour, sugar, salt, and yeast. Whisk with a balloon whisk and set aside. To a microwaveable bowl add the milk, unsalted butter, vegetable oil and vanilla extract then microwave for 50 secs or until the milk is warm and butter has melted. If you have a thermometer then you can test the temperature which should be around 43oC.
Pour the wet ingredients into the mixing bowl with the dry ingredients and using a dough hook mix the ingredients. While the ingredients are mixing add in the egg and continue to mix until a dough forms. The dough will be quite sticky so pour the dough onto a floured surface using a large spoon. Sprinkle some flour onto the dough and begin to knead for around 4 minutes or until the dough is smooth and slightly springy.
To a bowl, add a couple drops of vegetable oil and use your hand to spread the oil to ensure it covers all the inside of the bowl, this is to ensure the dough doesn’t stick. Add the dough to the bowl and cover with cling film (plastic wrap). Leave the dough to rise in a warm area for 2 - 3 hours or until the dough has doubled in size. (refer to recipe tips).
Prepare and add the filling: Whilst the dough is rising, you can prepare the filling. To a small bowl, unsalted butter, soft brown sugar and cinnamon then mix and set aside until needed. The butter must be very soft to combine well. Once your dough has doubled in size, flour a surface and roll out the dough into a square shape which should be around ½ a centimetre or ¼ of a inch thick. Using a palette knife, smooth the butter, sugar and cinnamon mixture onto the dough. Ensure it covers the whole surface.
Roll and cut the dough: Tightly roll up the dough and cut into 9 even rolls (firstly, mark where you want to cut with a knife). Place them in a 8 x 8 baking dish or tin and ensure there is equal space between them all as they will expand. Cover them and place them somewhere warm and draft free for 1 - 2 hours.
Bake the rolls: Once the rolls have expanded, preheat the oven to gas mark 4/350oF/180oC/160oC fan and bake for 30 - 35 minutes until lightly browned. If after 20 minutes they look like they are browning to quick, then cover them with foil for the last 10 minutes..
Make the glaze: Whisk the icing sugar and milk together and drizzle or spread over the warm rolls. Cover with foil until you’re ready to serve.