Sift the cocoa powder into a bowl or directly into a small saucepan to remove any clumps.
Add the sweetened condensed milk, butter, and a pinch of salt to the sifted cocoa.
Stovetop method: place the saucepan over medium-low heat and stir constantly until the butter is melted and the mixture is very smooth and thick.
Microwave method: place the mixture in a microwave-safe bowl and heat on high for 1 minute; stir, then continue in 30-second bursts, stirring between each, until smooth.
Remove from heat, stir in the vanilla extract, then thin the sauce by stirring in 1/4 to 1/2 cup milk until you reach the desired consistency.
Serve warm as a topping for desserts or allow to cool slightly before storing.