Take your water or milk of choice and heat it in a saucepan over the stove on medium-low (or nuke it in the microwave in 20-second increments at 40% power), warming it with either method until it’s just a bit too hot to touch (this will take a couple minutes). Do not let it boil, as it can ruin the milk (fine with water).
This is the real trick to the best Mexican hot chocolate (even if you’ve got the premade disks, like I do): chop your chocolate very small, and heat the milk by itself. So while your liquid is heating, shave or chop up your chosen chocolate, whether it comes in bar, disk, or chip form, until it’s in little slivers.
Once just starting to bubble, add in all of your chocolate, corn starch, and spices, and stir until well-combined (about 30 seconds). Then turn off the heat and move the pan to a different surface, letting the pan or mug sit alone for a minute. Don’t touch it. This rest allows the cacao paste or chocolate to fully melt naturally, and if you over-heated your liquid, it could burn the chocolate or even separate the cacao solids from the cocoa butter, so stick to a low heat. Do this even if you used cocoa powder, as it will help the cornstarch thicken properly.
After a minute, slowly stir or whisk your drink together, combining the milk and chocolate from the bottom of the container up. If the fat and solids in the chocolate do separate, never fear. Just use a high-powered whisk or an immersion blender to re-combine everything; this will also make for a frothier drink (more traditional, in fact). This is when I usually add a pinch of salt to contrast the sweetness, but serve your Mexican hot cocoa however you’d like and enjoy!