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1. To make the biscuits: Preheat the oven to 450°F. Grease a baking sheet.
2. Whisk together the flour, baking powder, sugar and baking soda in a large bowl. With a pastry blender or fork, cut in the butter until the mixture is crumbly. Stir in the buttermilk and mix until a soft dough forms. Turn the dough out onto a clean work surface dusted with flour and pat into a ¾-inch-thick circle. Using a 2-inch round cutter or glass, cut the dough into 12 biscuits, gently reshaping the scraps as necessary. Place the biscuits on the prepared baking sheet and bake for approximately 8 minutes or until puffed and golden brown. Transfer to a wire rack to cool slightly.
3. To make the chocolate gravy: Whisk together the sugar, cocoa powder, and flour in a medium saucepan. Slowly whisk in 3 cups of water, followed by the vanilla. Turn the heat to medium and bring the mixture to a boil. Reduce the heat to low and simmer for 10 minutes, whisking constantly. To create a thicker gravy, blend together the cornstarch with 2 tablespoons of cold water in a small bowl. Transfer this mix to the chocolate gravy and whisk the gravy over low heat until thickened.
4. To make the cocoa: Whisk together the sugar and cocoa powder in a soup pot. Whisk in 4 cups of water, followed by the milk. Turn the heat to medium and bring the mixture to a boil, whisking often. Turn off the heat.
5. To serve, cut each warm biscuit in half horizontally. Lay both halves, cut side up, in a bowl. Spoon the warm chocolate gravy over the biscuits and serve with a mug of hot cocoa.
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