In a mixing bowl, cream together the butter and sugar until well combined. Stir in the egg and vanilla extract. In another bowl, whisk together the flour, salt and baking powder. Then stir the dry ingredients in with the wet. Stir in the chocolate chips and cherry pieces. Cover and refrigerate for 1 hour or overnight.
On a baking sheet lined with parchment paper, spoon the cookie dough. Bake at 325°F for 14-16 minutes in the middle to upper 2/3 of the oven. Remove to a cooling rack. Enjoy.