In the bowl of a stand mixer, whisk milk and yeast to dissolve. Reserve 2 T beaten eggs and add remaining eggs, 2 c flour, 3 1/2 T sugar, butter and salt to bowl. Using the dough hook, knead for 6 min on low speed. Dough should be soft, shiny and a bit sticky. If it's too sticky and will not hold together, add flour a tablespoon at a time, until soft dough forms. Place dough into a greased bowl, cover with plastic wrap or a lid and refrigerate at least 4 hr or overnight for a better result. Cover and chill reserved egg, as well.
Place dough onto lightly floured work surface. Roll out into 12” x 16” rectangle, approx. 1/4” thick.
Working quickly, spread chocolate hazelnut spread evenly over dough, all the way to the edges.
Starting from a longer side, roll dough tightly into a log.
With a sharp knife, cut log in half crosswise. Place logs side-by-side.
Cross logs in the center.
Continue crossing until you reach the ends, approx. 3-4 times, to create a braid. Lightly press together ends.
Grease loaf pan with spray or butter before transferring braid to pan, fitting it snuggly inside.
Brush top with reserved egg, then cover. Let it sit at room temp for 1 hr.
Meanwhile, preheat oven to 350º. Pour water into small saucepan, add 1/3 c sugar and bring to a boil, stirring only once to dissolve. Once syrup is boiling, cook for 30 sec, then remove from heat and allow to cool.
Brush babka with egg a second time and sprinkle with chopped hazelnuts.
Bake 25 min, then rotate and continue to bake for 15 min more. If cake browns on top quickly, tent loosely with foil and finish baking.
Remove from oven and immediately brush generously with syrup.
Let cool in pan for 10 min then remove babka and allow to cool completely on a wire rack.
Babka can be stored at room temp up to 4 days. Microwaving each serving 10-15 seconds is recommended if not serving soon after baking.