Pour 4 cups whole milk into a medium saucepan. Heat over medium-low to medium heat until steam rises and small bubbles form around the edge (do not boil), about 4–6 minutes.

Make cocoa paste

While the milk warms, whisk together 4 tablespoons unsweetened cocoa powder and 4 teaspoons granulated sugar in a small bowl. Add 2–3 tablespoons of the warm milk to the cocoa mixture and whisk until a smooth, lump-free paste forms.

Combine and melt chocolate

Pour the cocoa paste back into the saucepan with the remaining warm milk, whisking to combine. Add 3 ounces finely chopped bittersweet or semisweet chocolate and a pinch of salt. Continue to cook on medium-low, stirring frequently, until the chocolate is fully melted and the mixture is smooth and slightly thickened, 2–4 minutes. Do not boil.

Finish

Remove the pan from heat. Whisk in 1 teaspoon vanilla extract. Taste and adjust sweetness: add up to 1–2 teaspoons more sugar if desired. If making a flavored variation, add 1/8 teaspoon peppermint extract here for peppermint hot chocolate.

Serve

Ladle hot chocolate into four mugs (about 1 cup each).

Optional Finishes & Garnishes

Top each mug with a generous dollop of whipped cream (about 1/4 cup per mug) if using. Sprinkle mini marshmallows over the whipped cream or directly into the hot chocolate (about 1–2 tablespoons per mug).

Dust a light sprinkle of cinnamon and chocolate shavings over the top for aroma and presentation. For a peppermint touch, garnish with crushed peppermint candy (optional) in addition to the 1/8 teaspoon peppermint extract added earlier.