Warm the dairy base: In a medium saucepan, add the milk and heavy cream.
Set over medium heat and warm until steaming and small bubbles appear around the edges. Do not boil.
Whisk in cocoa and sugar: Sprinkle in the cocoa powder and 2 tablespoons of sugar. Whisk well to dissolve any lumps.
Taste and add the remaining tablespoon of sugar if you prefer it sweeter.
Melt the chocolate: Add the chopped dark chocolate. Whisk slowly until it melts completely and the mixture looks glossy and smooth.
Add caramel and salt: Stir in the salted caramel sauce and 1/4 teaspoon sea salt. Keep whisking until fully combined.
The hot chocolate should be thickened slightly and smell like chocolate fudge.
Finish with vanilla: Remove the pan from the heat and stir in the vanilla. This keeps the flavor bright and warm.
Add the rum: Pour in the rum and whisk to blend. Start with 2 ounces, then taste and add more if you want a stronger kick.
Serve: Divide into two large mugs.
Top with whipped cream, a drizzle of caramel, and a sprinkle of flaky salt. Serve immediately while it’s luxuriously warm.