Preheat the oven to 325°F (160°C). Lightly grease and flour a 9-by-5-inch (23 cm x 12 cm) loaf pan, tapping out any excess flour.
In a glass measuring cup, lightly beat the eggs with the vanilla. In a medium bowl, whisk together 1½ cups of flour, baking powder, and salt.
In a large bowl, use a handheld mixer to beat the butter and sugar at medium-high speed until fluffy, about 3 minutes. With the mixer on medium-low speed, gradually beat in the egg mixture until fully incorporated.
Add the flour mixture in three batches, beating at low speed between each addition until just incorporated. Continue to beat for an additional 30 seconds.
Spread one-third of the batter in the prepared pan, then layer half of the Nutella on top. Repeat with another third of the batter and the remaining Nutella. Finally, top with the remaining batter. Lightly swirl the Nutella into the batter using a butter knife, taking care not to overmix.
Bake the cake for about 1 hour and 15 minutes, until a toothpick inserted in the center comes out clean.
Bake the cake for about 1 hour and 15 minutes, or 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, turning it right side up, and let it cool completely, about 2 hours. Cut the cake into slices and serve.