In a small saucepan, whisk together the unsweetened cocoa powder, granulated sugar, and a pinch of salt. Whisking them while they are still dry helps break up any large clumps of cocoa powder before any liquid is added, ensuring a smoother drink.
Slowly pour in the milk while whisking constantly. Place the saucepan over medium-low heat. Continue to whisk until the cocoa powder is fully incorporated and the mixture begins to steam slightly. Avoid letting the liquid come to a boil.
Add the semi-sweet chocolate chips to the saucepan. Continue to stir frequently with a whisk or a spoon until the chocolate chips are completely melted and the liquid is smooth and hot. Keeping the heat low ensures the chocolate melts evenly without scorching the milk.
Remove the saucepan from the heat immediately. Stir in the pure vanilla extract. This adds a layer of aromatic sweetness that rounds out the chocolate flavor perfectly. Give it one final whisk to make it extra frothy before pouring.