Preheat the oven to 450ºF. Line a baking sheet with parchment paper or a silicone baking mat.
Microwave the frozen cherries for 30 seconds. They should come out cold, no longer frozen, and surrounded by a fair amount of juice. Strain and reserve the juice (you need this for the icing). Cut your cherries into quarters.
In a medium mixing bowl, combine the self-rising flour, sugar, chocolate chips, and cherries. Stir to combine and coat the cherry bits with flour.
Grate cold butter into the self-rising flour mixture, and toss with your hands to combine..
Fold in the milk. When it's mostly combined, turn out onto a floured counter. Fold 7 times until cohesive and all the dry mix is incorporated.
Form into a 1-inch thick circle. Cut into 8 equal wedges. Place on a lined baking sheet with 2 inches between each.
Bake for 13 to 17 minutes. Allow to cool completely.
In a small bowl, whisk together the powdered sugar with 2 Tablespoons of the reserved cherry juice. Add juice or powdered sugar until your icing is thick enough that your whisk leaves trails for 5 seconds and then settles into a smooth surface.
Transfer the icing to a plastic baggy, and snip the tiniest bit of the corner off. Pipe drizzles of icing on each scone.
Allow the icing to set for at least 15 minutes before serving.