Arrange a rack in the middle of the oven and heat the oven to 350°F. Line a 9x5-inch loaf pan with parchment paper so it hangs off two sides to form a sling. Coat the pan and parchment with cooking spray.
Place 8 tablespoons unsalted butter in a small microwave-safe bowl and microwave on high power in 10-second increments until melted. (Alternatively, melt on the stove.) Mash 3 bananas in a large bowl with a fork or potato masher until smooth (about 1 cup mashed banana). Add the melted butter, 1 cup granulated sugar, 2 large eggs, 1/4 cup milk, and 2 teaspoons vanilla extract, and stir to combine.
Add 2 cups all-purpose flour, 1 teaspoon baking soda, and 1/2 teaspoon kosher salt. Stir with a rubber spatula just until no dry spots remain. Fold in the chocolate chips.
Transfer half the batter to the prepared pan. Using a spoon, dollop 1/3 cup of the Nutella onto the batter. Swirl the Nutella into the batter with a skewer or toothpick. Top with the remaining batter. Dollop the remaining 1/3 cup Nutella onto the batter and swirl with the skewer or toothpick.
Bake until a toothpick inserted in the center comes out mostly clean with a few moist crumbs attached, 55 to 65 minutes. Let cool 20 minutes in the pan, then flip the bread out of the pan onto a wire rack and let cool completely before slicing.