Laminated Brioche Cinnamon Buns with Peach Compote and Brown Butter Streusel

BRIOCHE DOUGH

1. In a small bowl, combine the yeast, milk and 2 tablespoon of the sugar. Mix well, and leave to sit for 10-15 minutes, or until foamy.
2. In the bowl of a stand mixer fitted with the dough hook, combine the flour, salt, cinnamon, and remaining 2 tablespoon sugar. Mix briefly to combine. Add the eggs, vanilla, and foamy yeast mixture to the bowl. Mix on low for 2-3 minutes, until the dough is starting to come together. It may look slightly dry but do not worry - it will mix together nicely in the next steps. Increase the mixer speed to medium, and mix for another 10 minutes, until the dough is soft and smooth. 
3. Reduce the mixer speed to low, and add the butter a little at a time, waiting until it is fully incorporated into the dough before adding the next piece. This process should take 3-4 minutes. Once the butter is fully incorporated, increase the mixer speed to medium, and mix for a further 5 minutes, until the dough is very soft and smooth. 
4. Transfer to an oiled bowl, and cover tightly with plastic wrap. Place in a warm spot until doubled in size, approximately 1 - 1 ½ hours, or overnight.

PEACH COMPOTE FILLING

1. Place all of the ingredients into a medium pan and place over medium heat. Bring to a boil, stirring occasionally, then roughly mash. Continue to cook, stirring frequently, fro 15 minutes, or until thick. Transfer to an airtight container and chill completely. Can be made ahead.

BROWN BUTTER STREUSEL

1. Preheat the oven to 350˚f / 180˚c. Line a baking sheet with parchment paper. 
2. Place the butter in a small pan, and place on the stove over medium heat. Heat, stirring occasionally, until the butter has melted. Continue to cook, until the butter begins to foam, smells nutty, and goes a deep golden brown colour. Remove from the heat and place in a medium heatproof bowl. Add the remaining ingredients, and mix well to combine. Using your hands, break up any large lumps. Spread evenly over the baking sheet, and bake until lightly golden and toasty, 10-15 minutes. Remove and allow to cool completely before storing in an airtight container.

ASSEMBLY

1. In a small bowl, combine the brown sugar, cinnamon, and salt. Turn the dough out onto a lightly floured surface, and roll into a 16”x26”(40cmx66cm). Lightly brush with butter, and sprinkle with half of the cinnamon sugar mixture. Fold into thirds like a letter, then roll out again into a 16”x26” (40cmx66cm) rectangle. Brush again with butter, and add the remainder of the cinnamon mixture. Spread the dough with a cup of the peach compote, and sprinkle with a cup of the brown butter streusel.
2. Starting on the SHORT side, roll up into a log. Place the log onto a parchment lined baking sheet, lightly cover with plastic wrap, and transfer to the freezer for 20 minutes. Alternatively you can chill it in the fridge for about an hour. If your dough is still quite cold if you did an overnight rest, you can skip this step if you like, but I find it helps a lot with keeping a nice tidy spiral.
3. Line a baking sheet with parchment paper. Trim the ends of the log of dough so that they are tidy. Using a very sharp knife, measure the log of dough, and cut into 12 even pieces. Arrange on the baking sheet.
4. Lightly cover the buns with plastic wrap, and place in a warm spot for 45 minutes to an hour, until they are puffy. While the buns are rising, preheat the oven to 350°f / 180°c.
5. Bake the buns for 30 to 35 minutes, until golden brown. Remove from the oven and allow to cool.
6. To make the glaze, combine all the ingredients into a small bowl. Adjust the amount of cream if needed to make a consistency that will drizzle.
7. Drizzle the glaze over the buns. Store leftover buns lightly covered at room temperature. Rewarm in the microwave briefly before eating if desired.