Preheat the oven to 325°. Lightly grease and flour a 9-by-5-inch loaf pan, tapping out any excess flour. In a glass measuring cup, lightly beat the eggs with the vanilla. In a medium bowl, whisk the 1 1/2 cups of flour with the baking powder and salt.
In a large bowl, using a handheld mixer, beat the butter with the sugar at medium-high speed until fluffy, about 3 minutes. With the mixer at medium-low speed, gradually beat in the egg mixture until fully incorporated. Add the flour mixture in 3 batches, beating at low speed between additions until just incorporated. Continue to beat for 30 seconds longer.
Spread one-third of the batter in the prepared pan, then spread half of the Nutella on top. Repeat with another third of the batter and the remaining Nutella. Top with the remaining batter. Lightly swirl the Nutella into the batter with a butter knife. Do not overmix.
Bake the cake for about 1 hour and 15 minutes, until a toothpick inserted in the center comes out clean. Let the cake cool in the pan for 15 minutes. Invert the cake onto a wire rack, turn it right side up and let cool completely, about 2 hours. Cut the cake into slices and serve.