Preheat oven to 210 degrees (fan-forced). Lightly grease a 20cm round cake tin and set aside.
Place the cold butter and self raising flour into the Thermomix bowl. Mix on Speed 5, 10 seconds. Scrape down the sides of the bowl and repeat 2 more times.
Mix on Interval (knead) function for 1 minute (whilst pouring in the milk).
Sprinkle some extra flour onto a board or bench. Roll the dough out into a 5mm thick rectangle.
Place the room temperature butter, brown sugar and cinnamon into the Thermomix bowl.Mix on Speed 4 for 20 seconds. Scrape down the sides of the bowl and repeat.
Spread the cinnamon butter mixture onto the dough. Sprinkle over the chopped apple.
Roll the dough up into a tube (lengthways). Use a sharp knife to cut the roll into 8-10 pieces. Place the pieces cut side up into the prepared cake tin (allow the rolls to touch one another as this will help them to rise).
Bake for 15 minutes or until golden brown. Allow to cool slightly in the tin.
Place the icing sugar and 2 tbs hot water into the Thermomix bowl. Mix on Speed 6 for 10 seconds. Scrape down the bowl and repeat 2 more times. Use a spoon to drizzle over the buns. Note: If the mixture is still too thick, add another tablespoon of hot water and mix for a further 10 seconds.
Serve warm or cold.