In a bowl, combine the warm milk, yeast, and a teaspoon of sugar. Let it sit for about 5 minutes, or until foamy.
In a large mixing bowl, whisk together the flour, remaining sugar, and salt.
Make a well in the center and add the melted butter, eggs, and the yeast mixture. Mix until a dough forms.
Knead the dough on a floured surface for about 10 minutes, until smooth and elastic. Place in a greased bowl, cover with a damp cloth, and let it rise in a warm place for about 1-2 hours, or until doubled in size.
Once risen, punch down the dough and roll it out into a rectangle about 1/4 inch thick.
Spread the chocolate hazelnut spread over the dough, leaving a small border on all sides. Sprinkles the chopped hazelnuts, cocoa powder, and vanilla extract over the spread.
Roll the dough tightly from the long side to form a log. Pinch the ends to seal.
Slice the log in half lengthwise to create two pieces. Twist the pieces together and place in a greased loaf pan.
Cover with a cloth and let it rise for another 30-45 minutes. Preheat your oven to 350°F (175°C).
Before baking, whisk the remaining egg and brush it over the top of the dough for an egg wash.
Bake for 30-35 minutes or until golden brown. Let cool in the pan for 10 minutes before transferring to a wire rack.
Notes
Slice the babka and arrange it on a decorative plate. Dust the top with powdered sugar for an elegant finish. Serve warm with additional chocolate hazelnut spread on the side for dipping.