Preheat oven to 425 degrees F. Line baking sheet with parchment paper.
Place flour, sugar, baking powder, baking soda, salt, cinnamon, and nutmeg in the bowl of a food processor fitted with a metal blade. Process with six 1-second pulses.
Remove cover of food processor and sprinkle the butter evenly over the dry ingredients. Cover and process with 12 1-second pulses. Transfer contents to a large bowl.
Stir heavy cream into the flour mixture, adding up to 2 additional tablespoons of heavy cream just until moistened. Fold in cinnamon chips and knead the dough by hand 6 to 8 times (do not overprocess or scones will be tough) then turn the dough out onto a lightly floured work surface. Divide dough in half. With lightly floured hands press each half of dough into a 7-inch round. With a sharp knife or pizza cutter, cut the dough into 6 wedges. Repeat with remaining dough.
Place wedges on the prepared baking sheet. Brush the scones with 1 tablespoon of heavy cream and sprinkle lightly with turbinado sugar.
Bake in preheated oven 10 to 13 minutes or until tops of scones are a lightly browned. Transfer to a wire rack for at least 10 minutes before glazing.
While the scones are cooling, make glaze. Combine 1 tablespoon heavy cream, and confectioners’ sugar until you achieve a thick, opaque icing. Drizzle over scones and serve.