Bring the eggs and butter up to room temperature before beginning
Warm the milk either in the microwave or in a saucepan until it is warm to the touch, but not too hot
To the warm milk, add 1 tablespoon of the sugar and the yeast. Give it a little stir and let the yeast activate for about 10 minutes, or until it is foamy and fragrant
In a KitchenAid or stand mixer, add the flour, salt, sugar, vanilla and milk/yeast mixture. On low-medium speed, mix all of those ingredients until well incorporated
Add in eggs one at a time and let the dough mix
After the eggs are incorporated, add half of the softened butter and mix for several minutes
Add the rest of the butter and run the mixer for about another 3 minutes
If the dough seems wet or sticks to the sides of the bowl, add 1 tablespoon of flour at a time and mix for another minute or so, until the dough pulls away from the sides of the bowl.
Transfer the dough to a large buttered mixing bowl and cover with plastic. Place it in a warm place and let it rise for 2 hours. It won't quite double in size, but it should rise a little.
Punch the dough down, re-cover it and place it in the fridge for at minimum 4 hours, preferably let it rest in the fridge overnight.
After it has rested, take half of the dough and place it on parchment paper. Roll it into a thin rectangle (about 10"x18" and ⅛" thick roughly). It will be a stiff dough, so you will have to use a rolling pin and it may take a few minutes.
Spread ½ cup of the Nutella evenly on the rolled babka dough even up to the edges.
Tightly roll the babka lengthwise and pinch all of the seems closed
Place the rolled babka into the freezer for 10 minutes while you work on the other half of the babka dough
Repeat the steps for rolling out the babka
Pull the first prepared Nutella babka dough out of the freezer and with a serrated knife, cut it lengthwise so that you have 2 long halves.
Braid the babka by placing one of the halves across the other and twisting them together (video in post)
Place the braided babka in a well butter bread loaf pan
Repeat with the other babka loaf
Cover and let the babka loaves rise in a warm place for another 1-2 hours
Preheat the oven to 350° and bake the babka bread loaves for 25-30 minutes, or until golden brown on top