In a medium bowl, whisk together granulated sugar and cocoa powder, being sure to whisk out any lumps in the mixture.
In a medium saucepan, melt butter over medium heat. Whisk in milk, and the combined sugar and cocoa powder.
Cook, whisking continuously, until the mixture begins to bubble around the edges and thicken, 3 to 8 minutes. Remove from heat and stir in vanilla extract.
Sauce will continue to thicken as it cools. Let it sit for 3 to 5 minutes before serving.
Serve poured over something delicious, and enjoy!