Add your milk, yeast and sugar to the mixing bowl to activate the yeast. Mix for 2 minutes / 100°F|37°C / speed 1.
Add 1 egg, bread flour, butter and salt. Knead using the knead mode for 1 minute.
Check dough for the consistency, then add more water or flour depending on the desired consistency. Knead again using the knead mode for 1 minute.
If necessary, knead in a little more flour or water until it reaches the right consistency. Take the dough out, shape it into a ball and put it into a bowl covered by a tea towel. Allow the dough to prove for at least 1 hour until it has doubled in volume. Clean the mixing bowl.
Roll your dough into a rectangle for half an inch thick, before sprinkling over the sugar and cinnamon evenly across the dough. Roll into a pinwheel, then cut into 8, flatting out slightly with your hand. Place on a baking sheet and allow to prove for 30 minutes.
Preheat your oven to 200°C / 410°F. Glaze with the remaining beaten egg, then bake in the oven for 20 minutes till golden.
Add your softened butter into the mixing bowl, along with the icing sugar. Insert the butterfly whisk and cream your butter and sugar for 1 minute 30 seconds / speed 4. Scrape down the sides.
Add your lemon juice into the mixing bowl, then mix the icing again for 20 seconds / speed 4. Once done, drizzle the icing over the buns and serve.
Serve warm or keep at room temperature till eaten.