For the hot chocolate, combine the milk, sugar, and ground cinnamon in a saucepan over medium-high heat.
Bring to a light simmer and add the chocolate chips, adding 1/2 ounce at a time to balance the chocolate level of your drink. I like my drink to be extremely chocolatey so I put the full amount.
In a cup, combine the hot chocolate, milk, and Irish cream. Top with whipped Irish cream.