Preheat your oven to 350°F (175°C). Grease and flour your 9x13-inch baking pan to prevent sticking.
In a large mixing bowl, beat the softened butter and granulated sugar together until light and fluffy, about 3 to 5 minutes with an electric mixer.
Add the eggs, one at a time, mixing well after each addition to ensure even distribution.
In a separate bowl, whisk together the sifted all-purpose flour and baking powder. Gradually add this to the butter mixture, alternating with the milk, beginning and ending with the flour mixture.
Gently fold in the chopped walnuts using a spatula, ensuring they are evenly distributed throughout the batter.
Pour the batter into the prepared baking pan and bake for 30 to 35 minutes or until a toothpick inserted into the center comes out clean. Allow the cake to cool completely on a cooling rack.
While the cake cools, prepare the glaze by whisking together the melted butter, powdered sugar, vanilla, and milk until smooth and glossy.
Once the cake has cooled, pour the glaze evenly over the top, allowing it to drip down the sides. Sprinkle the remaining chopped walnuts on top for added crunch.