Finely chop 4 ounces of semi-sweet chocolate with a sharp knife and set it aside in a medium heatproof bowl.
In a small saucepan over medium heat, combine 1 cup of whole milk, 1/2 cup of heavy cream, 2 tablespoons of sugar, and a pinch of salt, then whisk constantly until the mixture is steaming hot and the sugar has fully dissolved, about 3-4 minutes.
Reduce the heat to low and slowly pour the hot milk mixture over the chopped chocolate, letting it sit for 1 minute to soften the chocolate.
Whisk the chocolate and milk mixture vigorously until the chocolate is completely melted and the mixture is smooth, glossy, and uniform.
Remove from heat and stir in 1/4 teaspoon of vanilla extract until fully incorporated.
Pour the hot chocolate immediately into two mugs and top with a dollop of whipped cream, if desired.