Whisk the cocoa powder, all-purpose flour, granulated sugar, and salt together in a medium mixing bowl to remove any large clumps.

Slowly pour the milk into the dry mixture while whisking constantly until the liquid is fully integrated and smooth.

Transfer the combined mixture into a medium saucepan and place it over medium heat.

Stir the mixture constantly with a whisk to prevent burning or settling at the bottom of the pan.

Continue cooking until the gravy transitions from a thin liquid to a thick, glossy consistency that coats the back of a spoon.

Remove the saucepan from the heat and immediately stir in the softened butter and vanilla extract until fully incorporated.

Split warm biscuits in half and ladle the hot gravy generously over the top before serving immediately.