Preheat the oven to 450 degrees . In a medium bowl, whisk the flour, baking powder and salt. Refrigerate the flour mixture 5 minutes. Coarsely grate the frozen butter into the flour mixture. Using your fingertips and working quickly to prevent the butter from melting, rub the butter into the flour. Add the milk; stir just to blend.
Divide the dough in half. On a floured surface or in a bowl, sprinkle the hot-chocolate mix over one dough half; knead gently to mix in the chocolate. Pat the plain and chocolate doughs into disks, each about 1/2 inch thick. Using a juice glass or a 1 1/2-inch cookie cutter, cut the dough into rounds. Gather scraps; cut out more biscuits.
Arrange biscuits on a parchment-lined baking sheet, spacing 1 to 2 inches apart. Bake until golden brown, 12 to 14 minutes.