- In the bowl of the stand mixer, put the water and the yeast. Leave to rise for 5 to 10 minutes.
- Meanwhile, in another bowl, mix the milk, melted butter, sugar, salt and one egg. Add the liquid ingredient mixture to the yeast.
- Add the flour. Using the hook, knead the dough for 5 to 6 minutes, until it becomes soft and sticky.
- Brush a bowl with vegetable oil and place the dough in it. Cover with a clean cloth and let the bun dough rise for 1 ½ to 2 hours (or until the dough doubles in volume).
- In a bowl, mix brown sugar and cinnamon together. Set aside.
- Brush a 13 in x 9 in pan with soft butter. Set aside.
- On a generously floured work surface, roll out the risen dough to obtain a 50 cm x 35 cm (20 in x 14 in) rectangle.
- Brush the melted butter all over the dough and evenly distribute the brown sugar and cinnamon mixture.
- Firmly roll the dough into a roll 50 cm (20 in) long.
- Cut the roll into 12 thick slices.
- Place the buns in the buttered mold.
- Let rise, uncovered, in a warm, humid place for about 2 hours (or until the buns are puffed up and touch each other).
- Preheat the oven to 180°C (350°F).
- Brush the puffed buns with the beaten egg.
- Bake the buns for 20 to 25 minutes or until nicely browned.
- Take the buns out of the oven and let them rest for 10 minutes.
- In a bowl, combine all the ingredients for the glaze and, using an electric mixer, beat until smooth and creamy.
- Generously brush the brioches with the glaze. Serve.
Chief secret
To make the dough rise faster, put 1 cup of water in the microwave and bring to a boil for 2 minutes. Take out the cup of hot water, cover the bowl containing the dough with a clean cloth and put it in the microwave. The warm, humid environment will allow the dough to rise faster.