In a small saucepan over low heat, combine the milk, chocolate, brown sugar, chiles, and cinnamon stick. Cook, stirring occasionally, until the chocolate is melted and well combined, 10–12 minutes.
Drizzle the cajeta around the rim of an oven-safe mug, letting a little bit drip down the outside.
Carefully strain the hot chocolate through a fine-mesh sieve into the mug. Stir in the vanilla. Spoon the marshmallow fluff on top.
Using a hard torch, carefully toast the top of the marshmallow fluff until golden brown. Shave more chocolate on top, if desired.