Place the butter and milk in a sauce pan over a low heat, stirring occasionally until the butter has melted. Remove from the heat and leave to cool until lukewarm.
Place the flour, yeast and caster sugar in a large bowl and stir to combine. Once the milk has cooled, make a well in the flour, crack in 2 eggs and pour in the milk. Mix to combine to form a sticky dough. The dough will be very sticky, but do not add more flour!
Oil the work surface with a teaspoon of olive oil so the dough does not stick. Tip the dough onto the work surface and knead vigorously for 10 minutes. Once again, do not add more flour. As you knead, the dough will become less sticky and eventually a smooth elastic dough will form. place the dough into a lightly oiled bowl and cover with cling film. Place the bowl in a warm place to prove for 1 hour.
While the dough is proving, prepare the filling. Mix brown sugar and the cinnamon with the softened butter until the sugar is combined. Feel free to add more cinnamon!
Once the dough has doubled in size, turn it out onto a lightly floured work surface. Roll the dough into a rectangle, approximately 40x28cm. Spread the cinnamon-sugar butter evenly over the dough.
Taking the long edge closest to you, roll the dough tightly into a cylinder. Slice the dough into 12 rolls and place on grease proof paper in a roasting tin. Cover with a cling film and leave to prove for another 30 minutes. Meanwhile preheat the oven to 180 °C.
Beat the egg and brush over the buns. Sprinkle with more cinnamon and a little brown sugar. Bake in the oven for 12-15 minutes or until golden brown.