In a medium-sized saucepan, pour in the whole milk and heavy cream. Place the saucepan over medium heat and warm the mixture until it becomes steaming—take care not to let it reach a boil as this could affect the texture.
Once steaming, gradually whisk in the unsweetened cocoa powder and sugar. Continue to whisk until both ingredients are completely dissolved and the mixture is smooth.
Add the semi-sweet chocolate chips to the saucepan. Keep whisking until the chocolate is completely melted and incorporated into the mixture, achieving a velvety texture.
Remove the saucepan from the heat and stir in the pure vanilla extract along with the non-alcoholic Irish cream-flavored syrup. Mix thoroughly and taste; adjust the sweetness by adding more sugar if desired.
Carefully pour the decadent hot chocolate into large mugs, filling them generously.
Finish off each mug with a lavish amount of whipped cream on top. For an extra touch of elegance, sprinkle with chocolate shavings or lightly dust with cocoa powder.
Notes
Adjust the sweetness by adding more sugar if desired.