Preheat your oven to 350°F (175°C) and grease a 9-inch round cake pan.
In a mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.
Add the eggs one at a time, ensuring to beat well after each addition. Stir in vanilla extract.
In another bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture and mix until just combined.
Gently fold in the chopped walnuts, making sure to distribute them evenly throughout the batter.
Pour the batter into the prepared cake pan and spread it out evenly.
Bake for about 25-30 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool before slicing and serving.