Preheat the oven to 450 degrees. In a large bowl, combine the flour, baking powder, baking soda, and salt. Use the back of a fork or a pastry cutter to cut in the cream cheese and butter until large, pea-sized clumps exist throughout. Stir in the chocolate chips and then add the buttermilk, stirring to combine. Dump the shaggy dough out onto a floured surface and used floured hands to gently pat the dough out into a 1” rectangle. Fold the dough in thirds like a letter and then pat it out again into 1” thickness. Use a 2” biscuit cutter to cut out rounds of dough. Gently combine the scraps and then pat out that mixture to 1” thick again. Cut out additional rounds. Place the dough rounds onto a baking sheet and brush the tops with the melted butter. Place the pan in the oven, reduce the heat to 400, and bake for about 18-20 minutes or until the tops are puffed and golden. You may need to rotate the pan towards the end of baking if one size is darkening faster than the other. Allow the biscuits to cool briefly while you prepare the topping.
Beat the cream cheese and powdered sugar in large bowl just until smooth. Add a tablespoon or more or milk to get the icing a smooth, spreadable consistency. Smooth a dollop on each biscuit and serve immediately!