In a medium bowl, whisk together the all-purpose flour, baking powder, salt and ground walnuts. Set aside.
In a large mixing bowl, beat the unsalted butter and sugar together until light and fluffy.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.
Gradually add the flour mixture to the butter mixture, alternating with the milk. Begin and end with the flour mixture. Mix until just combined.
Pour half of the white batter into the prepared bundt pan, then layer half of the chocolate batter on top. Repeat with the remaining white and chocolate batters. Swirl with a knife or skewer to create a marble effect if you like.
Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for about 15 minutes, then invert onto a wire rack to cool completely.