Place the warm milk into the bowl of an electric stand mixer and sprinkle the yeast on top. Add the egg and egg yolk, melted butter and sugar and mix until combined.
Add in the flour and salt and stir. Once combined using the dough hook, knead on medium speed for around 8 minutes until you have a sticky but formed ball of dough that comes away from the sides of the bowl. If it is too sticky add a little more flour a tablespoon at a time.
Transfer to an oiled bowl and cover with cling film. Allow to rise somewhere warm for between one and one and a half hours until doubled in size.
Transfer to a floured surface and roll into a rectangle measuring around 9” x 15”.
Spread the butter over the dough leaving a border on the outside edge.
Mix the sugar and cinnamon then spread this over the buttered dough.
Roll the dough tightly starting at the 9 inch side and finish with the seam underneath.
Cut off the rough ends then slice into 9 equal slices.
Place into a greased and lined baking tin, cover and leave to rise again for a further 45 minutes.
Preheat the oven to 350 f then place the buns in the oven to bake for 25-30 minutes until golden on top but soft in the middle.
Allow to cool before frosting.
To make the frosting combine all the ingredients in a bowl and whisk with an electric whisk until light and fluffy. Spread onto the buns.