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For the dough, gently heat the milk and butter until the butter has just melted. Leave to cool until just warm to the touch (it shouldn’t be hot). Tip the flour into a large bowl with the yeast, cinnamon, sugar and a pinch of salt. Pour in the warm butter and milk mixture along with the egg, then combine with your hands until a dough forms. Tip the dough out onto a floured surface, and knead for about 10 mins until springy. Alternatively, you can do this in a stand mixer fitted with a dough hook – the dough will only require about 5 mins of kneading using this method. Bring the dough together into a ball, then place in an oiled bowl. Cover with a clean tea towel and leave to rise for about 1 hr, or until doubled in size.
Meanwhile, beat the filling ingredients with a small pinch of salt using an electric whisk until completely combined. Set aside. Butter a 20cm springform or loose-bottomed cake tin. Tip the dough out onto a lightly floured surface and knead briefly to knock the air out. Leave to rest for a few minutes, then roll out to a 30 x 50cm rectangle, and lay it on the surface so the short edge is facing you. Spread over the filling so the dough rectangle is completely covered. Cut the dough into four strips down the length. Roll the first strip up into a tight spiral from the short end, then place the spiral at the short end of the second strip and roll this up into a spiral around the first. Place this larger spiral at the short end of the third strip and roll up again, then repeat with the final strip of dough. You should end up with one large cinnamon bun. Transfer to the prepared tin, cover with a clean tea towel and leave to rise for 45 mins-1 hr, or until it has risen by about a third.
Heat the oven to 200C/180C fan/gas 6. Put the cake tin on a baking tray and bake for 50 mins-1 hr until puffed up, golden and cooked through. Meanwhile, combine the icing sugar, vanilla and 3 tbsp water until you have a loose icing that can be drizzled. Leave the bun to cool in the tin for 10 mins, then remove from the tin, drizzle with the icing and leave to cool completely on a wire rack. Serve in slices, or let everyone pull it apart. Will keep in an airtight container for two days.