Preheat your oven to 400°F (200°C). Prepare a baking sheet by lining it with parchment paper for easy cleanup and to prevent sticking.
In a spacious mixing bowl, combine 2 cups of all-purpose flour, 1/4 cup of granulated sugar, 1 tablespoon of baking powder, and 1/2 teaspoon of salt. Use a whisk to blend the dry ingredients thoroughly.
Add the 1/2 cup of cold, cubed unsalted butter to the bowl with the dry ingredients. Work the butter into the flour mixture until it resembles coarse crumbs.
In a separate bowl, whisk together 1/2 cup of heavy cream, 1 teaspoon of vanilla extract, and 1/2 teaspoon of peppermint extract until well combined.
Make a well in the center of the flour mixture and pour in the cream mixture. Stir gently until the ingredients are just combined.
Gently fold in the 1/2 cup of semi-sweet chocolate chips and 1/4 cup of crushed peppermint candies until evenly distributed.
Lightly flour a clean work surface, then turn the dough out onto it. Knead the dough a few times until it just comes together.
Shape the dough into a circle, roughly 1 inch thick. Cut the circle into 8 wedges and transfer them to the prepared baking sheet.
In a small bowl, beat the egg until frothy. Brush the egg wash over the tops of each scone.
Bake in the preheated oven for 15 to 20 minutes, or until the scones are lightly browned and a toothpick inserted comes out clean.
Allow the scones to cool slightly on a wire rack before serving.
Notes
Serve warm on a festive platter, garnished with additional crushed peppermint candies.