Preheat oven to 375°. In the bowl of a food processor, combine 3 cups flour, 3 tbsp. sugar, baking powder, and salt; whirl until blended. Add 1/2 cup butter and pulse until fine crumbs form. Add cream and pulse just until dough comes together when you squeeze a clump.
Turn dough onto a floured surface and press to flatten slightly. Sprinkle chocolate chips over the top, then knead until incorporated, 6 to 8 turns. Pat dough out to 1 1/4 in. thickness. With a 2 3/4-in. round cutter, cut out shortcakes; gather dough and pat out again as needed to cut all 6 cakes, dusting surface with more flour as needed to prevent sticking. Set shortcakes slightly apart on a baking sheet, brush tops with melted butter, and sprinkle generously with sugar.
Dark Chocolate Sauce