Heat milk and butter together in the microwave for 30 seconds. Stir, and reheat another 30 seconds if needed until butter is mostly melted. Stir again until fully melted. Make sure it’s lukewarm—not hot—before adding to the bowl.
Add the milk mixture and egg to the flour mixture. Beat for 2 minutes, starting on low and increasing to high speed.
Scrape down the sides using a spatular. Add 120 g (1 cup) more flour and mix to combine.
Add the last 120 g (1 cup) of flour one spoonful at a time just until the dough comes together.
Knead the Dough:
Switch to the dough hook and knead for 9 minutes. The dough is still sticky before rising. Grease a large bowl lightly with sunflower oil. Place the dough inside and cover with a clean dish towel.
First Rise:
Let rise in a warm spot for about 1 hour or until doubled in size. (see Baking with Yeast - Tips for success)
Shape the Rolls:
Turn the dough onto a well-floured surface (avoid cold granite in winter—see tips below).
Roll into a rectangle approximately 30 x 45 cm using a rolling pin.
Cut into 12 long strips along the longer (45 cm) side.
Spread each strip with room-temperature butter (reserve 1 tbsp for sealing).
Mix the brown sugar and cinnamon, then sprinkle it over each strip and press gently to help it adhere.
Roll each strip tightly into a swirl and seal the edge with the reserved butter.
Second Rise:
Place rolls in a deep baking tray lightly sprayed with non-stick spray and then lined with parchment paper.
Cover and let rise for about 1 hour, or until puffy and doubled.
Bake:
Preheat oven to 170°C (340°F).
Bake for 25 minutes, until golden and baked through.
Make the Frosting:
Using the paddle attachment, mix all frosting ingredients until light and fluffy.
Spread over warm (not hot) cinnamon rolls. If you let them cool completely before frosting, they lose steam (literally), and dry out fast.