In a medium saucepan, melt the unsalted butter over low heat.
Once the butter is melted, remove the saucepan from the heat and sift in the powdered sugar and cocoa powder.
Gradually add the milk to the saucepan while continuously stirring with a whisk or spatula until the mixture is smooth and well combined.
Place the saucepan back on the stove over low heat and continue to cook the mixture, stirring constantly, for about 2-3 minutes until it thickens slightly.
Remove the saucepan from the heat and stir in the vanilla extract and a pinch of salt.
Transfer the chocolate fudge frosting to a mixing bowl and let it cool for a few minutes.
Once the frosting has cooled slightly, use an electric mixer or hand mixer to beat the frosting on medium speed for 1-2 minutes until it becomes creamy and smooth.
If the frosting is too thick, you can add a little more milk, 1 tablespoon at a time, until you reach your desired consistency.
Use the chocolate fudge frosting to frost cakes, cupcakes, brownies, or any other desserts of your choice.
Serve and enjoy the rich, chocolatey goodness of this homemade Chocolate Fudge Frosting on your favorite treats!