Melt the butter in a medium saucepan over low heat.
Whisk in the cornstarch until fully dissolved and smooth. For a thicker hot chocolate, use double the cornstarch.
Gradually pour in the milk while whisking, followed by the sugar. Use the maximum amount of sugar for those with a sweet tooth.
Increase the heat to medium-high and bring the mixture to a simmer, stirring constantly. The mixture will begin to thicken as it heats.
Once thickened, reduce the heat to low and stir in the chocolate chips. Continue stirring until the chocolate is completely melted and the mixture is smooth.
Serve hot. Store any leftovers in an airtight container in the refrigerator; the drink is also delicious when served cold.