Preheat your oven to 350°F (175°C). Grease and flour a cake pan.
In a mixing bowl, cream together the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition.
Stir in the vanilla extract.
In another bowl, whisk together the flour, baking powder, and salt.
Add the dry ingredients to the creamed mixture alternately with the milk, beginning and ending with the dry ingredients.
Fold in the chopped black walnuts.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 45 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then turn out onto a wire rack to cool completely.