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Preheat the oven to 375°F. Lightly grease a large baking sheet, or line it with parchment.
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Combine the flour, sugar, baking powder, baking soda, cinnamon and salt in a medium-sized bowl. Cut the butter into pats, and work it into the dry ingredients until the mixture is unevenly crumbly.
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Add the cinnamon chips, stirring to distribute them.
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Whisk together the egg and milk, and add to the dry ingredients in the bowl. Stir to make a cohesive dough.
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Transfer the dough to a lightly floured work surface, and divide it in half. Shape each half into a disc that's about 4 3/4" wide and a scant 1" tall.
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Place the discs on the prepared baking sheet. Brush them with milk, and sprinkle heavily with coarse sparkling sugar.
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Cut each disc into six wedges. Pull the wedges apart so there's about 3/4" between them; they'll expand as they bake.
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Bake the scones for 20 to 25 minutes, until they're set all the way through; break one open to be sure.
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Remove the scones from the oven, and cool them on a rack.
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While the scones are cooling, mix together the glaze ingredients, if using. Add enough milk to make the glaze a thick but pourable consistency. Drizzle over the warm scones before serving.
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Storage information: Store leftover scones, well wrapped, at room temperature for several days; freeze for longer storage.