In a saucepan over low heat, add chocolate and 1/4 cup of milk. Begin stirring with a large spoon until the chocolate’s melted.
Slowly add the rest of the milk until it’s well combined. Then add sugar and mix well.
Pour a small amount of the chocolate mixture into a cup and add the corn starch. Mix until well thoroughly blended. Add this mixture back into the pan and continue cooking over low heat until it becomes rich and creamy.
Pour ½ ounce each of Bailey’s Irish Cream into the shot glasses, followed by the hot chocolate mixture, then serve.