Start by making the babka dough. Heat milk to 100-110°F (about 30-90 seconds in the microwave). Stir in yeast and allow to sit for 10 minutes. Yeast will activate and become foamy.
Add remaining dough ingredients and milk/yeast mixture to a mixer fitted with a dough hook. Mix until combined and then allow the mixer to continue kneading for a further 10 minutes.
Transfer dough to a greased bowl and cover with a towel or plastic wrap. Leave to rise in a dry place for 8 hours or overnight.
Once the dough has risen, remove from the bowl and divide the dough (it will be sticky) into two equal halves. Prepare two loaf pans with parchment paper.
Mix the filling ingredients together and set aside.
Flour your work surface and rolling pin generously. Roll out half of the dough to about 16×10 inches and spread with half of the filling, leaving about ½-inch of dough bare on one of the short ends. Wet the bare dough with water and then roll the dough into a log starting on one of the longer sides.
Using a sharp knife, cut the log in half lengthwise. Pinch both halves together at one end, then cross one side over the other repeatedly until you reach the other end. Pinch that end together and fold the pinched end under the loaf to neaten it before carefully transferring it to one of the prepared loaf pans.
Repeat steps 6 and 7 with the remaining half of the dough.
Preheat the oven to 350°F and allow the 2 loaves to rise for 30 minutes.
After the dough has risen, whisk together the egg and water and brush over the tops of each loaf. Sprinkle tops with coarse sugar before putting in the oven for 40 minutes. Allow to cool before eating.
To make the caramelized bananas (optional, but encouraged): In a small pot over medium-low heat, melt butter with the sugar and cinnamon. Place banana slices in the mixture and use a fork to gently toss them until they’re fully coated. Cook for 4 minutes each side before removing and putting on top of your banana bread slices.
