Preheat the oven to 350°F.
Combine 1 cup of butter with the granulated sugar in a large mixing bowl. Using an electric hand mixer, cream the butter and sugar together until smooth and homogeneous.
Once the butter and sugar have been thoroughly creamed together, add the eggs. Mix again on a high speed until they are fully incorporated. Lower the speed and mix in the milk, and vanilla.
Add the flour, baking powder, baking soda, and ¼ cup of cocoa powder to the mixing bowl. Keeping the hand mixer on a low speed, whisk in the dry ingredients until they are fully incorporated into the batter.
Grease a 9x13 inch baking dish with butter or nonstick cooking spray. Pour the cake batter into the dish and bake for 45 minutes.
Remove the cake from the oven and allow it to cool in the fridge for 1 hour. When the cake has about 15 minutes of cooling time left, whisk together the remaining butter, cocoa powder, powdered sugar, and chopped pecans until smooth and creamy.
Use a spatula to spread the frosting evenly over the top of the cake.
Slice, serve, and enjoy!