Preheat oven to 425°F and line baking sheet with parchment paper or aluminum foil
In medium mixing bowl, mix together flour, sugar, baking powder, and salt. Grate in frozen butter. Use hands to gently combine flour and butter until course crumbles form. Add in cherries and chocolate.
In separate mixing bowl, combine sourdough starter and cream. Pour sourdough mixture into dry ingredients. Combine with a fork until a sticky dough forms.
Turn out dough onto a floured surface and gently knead to combine, being careful not to overwork the dough. Gently pat into an 8 inch circle and cut into 8 triangles (Alternatively, you can make drop scones by spooning and dropping the dough onto your baking sheet, which should make 10 - 15 smaller scones). Place your scones on your prepared baking sheet about 2 - 3 inches apart and and brush tops with heavy cream. Chill in the refrigerator for 15 minutes.
Remove from refrigerator and bake for 18 - 25 minutes until tops and edges are golden brown. Serve warm.