Pour the milk into a small saucepan and place over medium-low heat. Heat the milk to 120°F, then remove from the heat and transfer to a stand mixer fitted with a dough hook. Add the yeast and lightly stir. Leave the mixture to sit for 5 minutes.

When the 5 minutes have elapsed, add the sugar, salt, and eggs to the milk/yeast mixture and stir until just combine.

Set the mixer to it's lowest setting and add a cup of the flour. Slowly add the remaining flour ,1/4 cup at a time. Adding more flour only when the dough cleans the sides of the bowl. Once you approach the 2 1/2 cups mark, check how sticky the dough is. The dough should be tacky but not gooey. You may need the extra 1/2 cup of flour, or you may not. I always err on the side of sticky dough, because you can always knead in a little extra flour by hand later on. If your dough is too dry, it's harder to walk it back.

Once the flour is thoroughly integrated, you can start adding the butter. Add the butter a piece or two at a time. Once the butter is no longer visible, add another two pieces. Continue until all the butter is integrated. This can take up to 30 minutes. Be patient.

Transfer the dough to a well-floured surface and knead for another 5 minutes. Form the dough into a ball and set aside. Grease a large mixing bowl with butter and add the dough. Cover the bowl with plastic wrap and let rise in a warm place for 1 1/2 hours - 2 hours or until doubled in size.

While the dough is rising, make the filling.

Melt the butter in a large skillet over medium heat. Once the butter is bubbling, add the sugar, cinnamon, cloves, salt and nutmeg. Sauté until fragrant, about 2 minutes.

Add the ginger and carrot and sauté until softened, about 5 minutes. Remove the pan from the heat and stir in the slivered almonds.

Transfer the filling to a bowl and let cool completely.

Place the risen brioche dough on a floured surface and using a well-floured rolling pin, roll the dough out to a rough rectangle, about 1/4 of an inch thick.

Spoon the cooled filling onto the dough and spread it evenly with the back of the spoon. Be sure to leave a 1-inch border of bare dough along the edge closest to you.

Starting with the edge farthest from you, tightly roll the dough into a log. Place the log seam down and wrap in parchment paper. Place the log on a flat surface in the refrigerator and chill for 30 minutes.

Slice the chilled log into 9 evenly-sized buns. Place the buns in a 9 x 7-inch baking dish and cover with plastic wrap. Transfer the buns to the fridge and let rise for 3 hours or overnight.

Preheat the oven to 350°F.

Make the egg wash by whisking the yolk and cream together in a small mixing bowl. Using a pastry brush, brush the tops of the buns generously with the egg wash.

Place the buns in the oven and bake for 25-30 minutes or until golden. Transfer the buns to a cooling wrack and cool for 10 minutes before glazing.

Place the goat cheese in a stand mixer fitted with a whisk attachment. Add the sugar and whisk at a medium speed until a thick paste forms, about 3 minutes.

Increase the speed to high and add the heavy cream, salt and vanilla. Whisk until smooth and silky.

Pour the glaze over the warm buns and let sit for another 10 minutes. Sprinkle the buns with additional slivered almonds and serve immediately.