Preheat the oven to 325°.
Lightly grease + 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 + 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 + 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 + 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 + let cool completely, about 2 hours.
Cut the cake into slices + serve.