In a large measuring jug, stir together the milk, sugar, and yeast. Set aside and allow the yeast to foam and bubble up - about 5 minutes.
In a large mixing bowl, add the milk mixture, butter, egg, egg yolk, and vanilla, and whisk until combined. Add the flour and salt, and mix until a sticky dough forms.
Transfer the dough to a well floured surface and knead for about 5 minutes, until smooth, elastic, and tacky. Your hand will stick to the dough when kneading, but should come off completely clean.
NOTE: If the dough gets too sticky to knead, sprinkle 1 teaspoon of flour at a time onto the dough or work surface until it becomes more manageable. Do NOT add more flour than you need because this will result in dry, dense bread.
Place the dough into a lightly greased large bowl, cover with clingfilm or a tea towel, and leave to rise in a warm place for 1 hour, or until doubled in size.
TIP: Preheat the oven to 43C/110F. Once heated, turn the oven off. Place the covered dough inside, and allow to rise in this warm environment.
Grease a 10-inch bundt pan and set aside.
For the Coating
Add the melted butter to one bowl. In another bowl, mix together the sugars and cinnamon.
Once the dough has doubled in size, gently deflate with your fist and transfer to a lightly floured surface.
Roll into a rough 9x9-inch square. Using a pizza cutter or sharp knife, cut the dough into 64 pieces and roll into balls.
TIP: Cut the dough square in half both ways. Cut each quarter in half both ways, then cut each square in half both ways. You now have 64 pieces of dough!
Dip each ball into the butter, and then roll them in the sugar mixture. Place the coated dough balls into the prepared bundt pan. Mix together any remaining butter with the cinnamon sugar, and pour over the dough balls.
Cover the pan with clingfilm and allow the dough to rise again in a warm place for 30 minutes.
Preheat the oven to 180C/160C Fan/350F/Gas 4.
Remove the clingfilm and bake for 30 - 35 minutes, or until golden brown and the internal temperature of the balls reach 88C - 93C (190F - 200F).
Cool for 5 - 10 minutes, then invert onto a large serving plate or cake stand.
For the Glaze
In a small mixing bowl, whisk together the icing sugar, vanilla, and cream until smooth and combined. Add more cream to thin out if necessary.
Drizzle over the warm bread and serve.
Notes
Storage: Monkey bread tastes best served warm on the day it is baked. Leftovers can be covered tightly and stored at room temperature for 1 day and in the fridge for up to 4 days.Freezing: Place uncoated shaped dough balls on a baking tray and refrigerate for 30 minutes. Once cold, place them in a freezer bag or freezer-safe container, and freeze for up to 3 months. Thaw in the fridge or at room temperature.Make ahead: Make the dough as instructed, and place into a lightly greased bowl. Cover with clingfilm and refrigerate overnight. In the morning, let the dough rise in a warm place for 1 – 2 hours before shaping and rolling into balls.