Preheat oven to 450F with the rack in the middle position.
In a food processor, pulse the flour, cocoa powder, instant coffee, sugar, baking powder, and salt together to combine.
Cut 5 Tablespoons of the chilled butter into 1/4 inch pieces. Place the remaining 1 Tablespoon of butter to the side (you will use it later). Scatter the butter pieces across the flour mixture. Pulse again in the food processor until it looks like coarse breadcrumbs with a few larger butter pieces, approximately 12 pulses.
Transfer the dough to a medium bowl. Add the heavy cream, peppermint extract, and 4 crushed candy canes (save the other 2 crushed candy canes for later). Combine with a spatula until the dough just comes together.
Option 1: For a round, clean edge, use a round cake pan. Scatter the remaining 2 crushed candy canes in the bottom of the cake pan. Press the chocolate dough on top of the candy canes into the pan in an even layer. Press firmly to make sure the dough is sticking together. Flip the pan over and forcefully tap the pan against a cutting board or clean counter, and the dough should come out in a clean, round disc.
Option 2: On a lightly floured cutting board, pour out the dough and press into a disc approximately 9 inches wide. Make it as even as possible. Press the remaining 2 crushed candy canes into the top of the dough.
Using a knife, cut the disc like you would a pizza into 8 wedges.
Melt the remaining 1 Tablespoon of butter in a small bowl or cup. Brush it across the top of the scones. Sprinkle the scones with some granulated sugar and/or sprinkles as desired.
Use the knife under each scone to move them to a parchment or silicone baking mat lined cookie sheet. Leave space between them as they will expand.
Bake the scones until cooked through, approximately 12-15 minutes.
Remove from the oven and let cool at least 10 minutes. The scones can be served warm or at room temperature.