Heat the oven to 450 degrees. In a medium bowl, stir the flour, baking powder, baking soda and salt.
Stir in the cheese and ham until coated. Stir in the sour cream and enough milk until a soft dough forms.
Turn onto a lightly floured surface and knead 5 to 7 times. Roll or pat into 3/4-inch thick circle. Cut with 2 1/2-inch round cutter dipped in flour.
Place the biscuits on an ungreased baking sheet. Bake for 10 to 12 minutes or until golden brown. Brush the tops of the warm biscuits with the melted butter.