Place all the ingredients in your bread machine, in the order recommended by your bread machine. Set your machine on the dough cycle.
When the cycle is done, empty the dough on to a floured board. Separate the dough into two equal portions. This recipe makes enough for two breads. Roll each ball of dough into a 16 by 12 rectangle.
Spread each rectangle of dough with the softened butter.
In a food processor, mince the hazelnuts until very fine. Add the rest of the filling ingredients and pulse until everything is combined. Sprinkle this filling over the dough.
Roll each rectangle up, until you have a 16 inch long rope. Pick up the two ends of the first rope and twist three times, to form a braid. Place on a parchment lined sheet pan. Repeat with the second rope. Cover the pan loosely with plastic wrap, and put it in a warm place to rise for one hour.
Preheat the oven to 350 degrees and bake for about 30 minutes, or until the babka is 180 degrees inside. Cool on a wire rack.