In a stand mixer bowl, combine the warm milk, sugar, eggs, and yeast. Mix briefly to combine. Gradually add the flour while mixing on low speed. Once incorporated, knead the dough for about 15 minutes.
Add the cold butter and salt halfway through kneading. Continue kneading until the dough becomes smooth, elastic, and slightly sticky. Place the dough in a lightly greased bowl, cover with plastic wrap or a clean towel, and let it rise in a warm place until it doubles in size (about 1–2 hours).
Divide the dough into two equal portions. Roll each piece into a thin rectangle on a lightly floured surface. Spread an even layer of Nutella over each rectangle, leaving a small border around the edges. Roll each rectangle tightly into a log. Pinch the seam closed to secure. Place each log seam-side down in a loaf pan lined with parchment paper. Cover the logs loosely with lightly oiled parchment paper to prevent sticking. Let the dough rise again in a warm place until it nearly reaches the top of the pans (30–60 minutes).
Preheat your oven to 325°F (165°C).
Bake the loaves for about 65 minutes. Check for doneness by inserting a toothpick into the center—it should come out clean or with just melted chocolate, not raw dough.