Pour the half and half and milk into a small saucepan and place over a lit burner set to low.
Simmer, whisking occasionally, until bubbles start to appear around the edges.
Whisk in the Sugar:
Gently whisk in the sugar until combined and simmer over low to dissolve.
Melt the chocolate:
An ounce at a time, drop the chocolate squares in, whisking until thoroughly melted each time. The liquid will thicken as you melt the chocolate in. Make sure you are whisking well to avoid scalding the milk or burning any chocolate to the edges or seams of the pan.
Stir in the liquor:
When the chocolate has all been melted in, remove from heat and pour in the rumchata and Kahlua.
Stir to combine.
Rim the glass:
Meanwhile, in a small bowl, whisk the powdered sugar and remaining milk together to form an icing.
Dip the rims of each mug into the icing to coat.
Place the now coated rims down into the brownie brittle with gentle force and turn, to coat the rim in crumbs.
Flip the mugs over and place a chocolate square in the bottom of each.
Pour and Serve:
Whisking once more, to make sure everything is well combined, pour the hot liquid carefully into each mug evenly.