Line a baking sheet or casserole dish with foil.
In a large bowl, combine powdered sugar and cocoa powder and stir until they seem reasonably well mixed. If the mixture seems like there are small clumps, you may sift it after its been measured.
Pour milk over sugar mixture but do no mix. Place cubes of butter on top. Microwave on high power 3-4 minutes until the butter has almost completely melted. If unsure, you can always microwave in short intervals to avoid over cooking the mixture.
Immediately remove mixture from microwave and stir well until thoroughly combined. You need to work fast because you want to spread the mixture while its still hot, but you want it to be fully mixed.
Once chocolate mixture is thoroughly mixed, stir in the walnuts and vanilla.
Immediately pour the warm fudge into prepared dish and spread to desired thickness. If using a baking sheet, you can form the fudge so that it only takes up a portion of the surface. It will only spread as far as you want, so make it as thick as you'd like the individual pieces to be. Alternatively, if you use a 10x10-inch pan, it will cover the entire surface.
Allow the fudge to fully set at room temperature. Our house is always freezing, so it doesn't take much time. If you live in a warm house, it may take several hours or even a bit of refrigeration.
Lift foil out of dish and transfer the fudge to a cutting board. Use a sharp knife to cut into squares.
Store in airtight container or plastic storage bag. Use parchment paper to separate layers, if needed.