In a medium-small (2 quart) saucepan, combine the milk or water and chocolate. Stir over medium heat until the mixture is steaming hot, and the chocolate more or less dissolved (there will still be small pieces). Pour into a Mexican chocolate pot (olla para chocolate) or a blender.
If using the Mexican pot, put a wooden molinillo in the pot and begin whipping the chocolate by rolling the handle quickly back and forth between your palms. The movement is a little like rubbing your palms against each other to warm them in cold weather—only here the molinillo’s wooden handle is between them. After about 2 minutes of vigorous beating, dip a spoon into the mixture to make sure the chocolate has dissolved (they’ll always be a few bits of chocolate on the bottom) and the mixture is foamy.
If using a blender, loosely cover (or take off the lid’s removable center piece—this eliminates dangerous pressure build-up when blending hot mixtures) and blend until the mixture is homogenous and foamy, about 30 seconds. Alternatively, use an immersion blender in a tall pitcher and blend until foamy.
Pour into cups, dividing the foam equally, and they’re ready to serve.
Working Ahead: Frothy Mexican hot chocolate waits for no one.