In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, instant yeast, and salt until they are well combined.
In a separate medium bowl, mix the warmed milk, melted butter, eggs, and vanilla extract using a whisk until the mixture is smooth and homogenous.
Gradually add the wet mixture to the dry ingredients, stirring with a wooden spoon or spatula until a soft, moist dough forms.
Transfer the dough to a lightly floured work surface and knead for 8-10 minutes, or until the dough is smooth, elastic, and slightly tacky to the touch.
Place the kneaded dough into a greased bowl, cover it with a damp cloth or plastic wrap, and let it rise in a warm area for about 1 hour, or until it has doubled in size.
Once the dough has risen, turn it out onto a floured surface and roll it into a large rectangle approximately 1/4 inch thick. Ensure the edges are well defined.
Evenly spread the chocolate hazelnut spread over the entire surface of the dough, leaving about a 1/2-inch border along the edges.
Sprinkle the chopped hazelnuts generously over the chocolate spread, distributing them evenly.
Starting from one long edge, carefully roll the dough tightly into a log, ensuring the filling remains inside. Pinch the seams closed to seal.
Use a sharp knife to cut the log in half lengthwise, creating two long pieces that reveal the delicious filling.
Twist the two halves together, keeping the cut sides facing up, and gently press them together to secure the twist.
Coil the twisted dough into a spiral shape and place it into a greased loaf pan, shaping it into a babka form.
Cover the pan with a cloth and allow it to rise again for about 30 minutes, ensuring it grows in size.
Preheat your oven to 350°F (175°C). Brush the top of the babka with the beaten egg to achieve a golden crust.
Bake the babka in the preheated oven for 30-35 minutes or until it is golden brown and a toothpick inserted in the center comes out clean.
Once baked, let the babka cool in the pan for about 10 minutes, then carefully transfer it to a wire rack to cool completely.