1. In a small saucepan over medium heat, combine the cocoa powder and sugar, then gradually whisk in the boiling water until the mixture is smooth and the cocoa and sugar are fully dissolved, about 2-3 minutes. (Scalding technique: the hot water blooms the cocoa — that is, it dissolves the cocoa solids and releases flavor compounds before the milk is added.)
2. Add the whole milk to the cocoa mixture. Heat over medium heat, stirring frequently, until the mixture is steaming and just below a simmer — small bubbles will appear at the edges of the pan and the surface will begin to tremble, approximately 8-12 minutes. Do not allow it to boil.
3. Add the brandy to the hot cocoa mixture and stir to combine.
4. Mill the cocoa: using a milk frother, immersion blender, or by pouring the hot liquid back and forth between two vessels held at a height, froth the mixture until it is foamy and uniform, about 30-60 seconds. (Milling is a period technique for frothing hot chocolate or cocoa by agitating it with a wooden whisk or molinillo; a modern frother achieves the same result.)
5. Ladle into warmed cups and serve immediately.
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