Place a saucepot over medium-high heat with three cups of milk. Heat the milk until it’s steaming, but don’t let it come to a boil.
While the milk is heating up, measure the cocoa powder into a mixing bowl and whisk together with the remaining cup of milk and vanilla until the mixture is smooth (getting the mixture smooth at this point will prevent lumps in the finished hot cocoa).
Remove the hot milk from the heat and add the chocolate morsels into the pot. Count to 10 slowly to give the chocolate a moment to melt, then whisk everything together to fully melt the chocolate. Add the cocoa powder-milk mixture to the pot and whisk to combine, heating the hot chocolate up over low heat if necessary.