To prepare dough, combine yeast, milk and sugar in the bowl of a standing mixer. Let stand for 10 minutes.
Whisk in egg, melted butter and salt.
Attach dough hook to the standing mixer. Add half of the flour and mix on low speed until thorough combined.
Add remaining flour and continue mixing until dough comes together. Increase speed to medium and knead until dough forms into a ball.
Cover with tea towel and allow to rise for an hour.
Roll dough to a large rectangle onto a floured surface. Brush another 1/2 stick of melted butter all over the dough.
Mix together apple, brown sugar and cinnamon in a small bowl, and sprinkle the mixture all over the dough.
Using a pizza cutter to cut the dough into 6 strips, then stack all the strips into one long stack. Cut the stack of strips into 6 small stacks. Place the stacks sideways into a greased loaf pan. Be sure not to cram the loaf pan, and leave space for the bread to expand.
Cover the loaf pan with a tea towel and allow to rise for another hour.
Preheat oven to 350F. Bake the bread for 40 minutes. Cover the top of the bread with aluminium foil about halfway through if it is browning too quickly.
Remove pan from the oven. Allow to cool for about 10 minutes on a wire rack. Run a knife alone the edges to release the bread from the pan.
Mix together the icing ingredients and drizzle over the top when the bread is still warm. Serve warm or at room temperature.