Bring cream and milk to a gentle simmer in a small pot.
Stir in rest of ingredients excluding chocolate and rum and whisk until fully incorporated.
Place chocolate pieces into another saucepan or heat-proof glass bowl and pour the hot liquid over. Stir to combine.
Blend with a hand immersion blender until frothy and light, or use a Latin American molinillo if you have one.
Stir in coconut rum. Taste test. If you like your hot chocolate sweeter, add a 1/2 teaspoon of raw cane sugar at a time until you reach your desired sweetness. It should be thick, but if you prefer yours more liquid, add some warmed milk or hot water.
Optional garnish: add whipped cream and top with toasted coconut and chocolate curls.