Place warm milk into the bowl of a stand mixer and sprinkle yeast on top. Add sugar, eggs and melted butter. Mix until well combined. With a wooden spoon, stir in flour to form a dough.
Place dough hook on stand mixer and knead dough on medium speed for 8 minutes. Dough will form into a ball.
Lightly oil a large bowl and transfer dough, cover with cling film and a clean cloth and allow dough to rise until doubled in size for approx. 90 minutes.
Once risen, transfer dough to a well-floured surface and roll out into a 33 x 23cm rectangle. Spread the softened butter on dough surface edge to edge.
In a small bowl, mix together the brown sugar and cinnamon. Use your hands to sprinkle and massage the sugar into the layer of butter on dough surface.
Tightly roll up the dough from the longest edge and place seam side down to secure the contents. Cut the edges off on either side of the roll, 1cm from each end to keep the scrolls uniform when baking. With a serrated knife, cut the roll into 9 even pieces.
Place the rolls into a lined and greased 22 x 22cm square or round pan. Cover with cling film and a clean cloth and allow to rise again for 30-40 minutes.
Preheat oven to 180°C. Remove cling film and cloth and bake for 20-25 minutes until slightly golden brown on the edges. Allow to cool while making the icing.
In a small bowl, whisk together the icing sugar, vanilla and hot milk until smooth. Spread over the cinnamon rolls and serve.