Finely chop the bittersweet chocolate and set aside.
In a medium saucepan, combine the whole milk, granulated sugar, and fine salt. Warm over medium heat, stirring occasionally, until steaming with small bubbles around the edges, 3–5 minutes; do not boil.
Remove the pan from the heat and add the chopped chocolate. Let sit for 1 minute to soften.
Whisk until the chocolate is fully melted and smooth, 1–2 minutes.
Return the pan to low heat and whisk constantly until the hot chocolate is uniformly hot and lightly steamy, 2–4 minutes (about 160–170°F); do not simmer.
Stir in the vanilla extract and taste; adjust sweetness if desired.
Pour into warmed mugs. Top with whipped cream or marshmallows and serve immediately.