Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper or silicone baking mats.
In a small bowl, sift the flour, cocoa powder, baking powder, salt and allspice together; keep at hand.
In a large mixing bowl beat the butter with an electric mixer on medium speed for 30 seconds. Add the sugar and continue to beat for 2 minutes, or until it is well blended into the butter. Reduce the mixer speed to low, add the egg and beat 1 minute more. Beat in the vanilla extract. The mixture may look curdled, but it will come together when you add the dry ingredients.
With the mixer at lowest speed, steadily add the flour mixture, beating for only a few seconds after it disappears into the soft dough. Give the dough a few stirs with a rubber spatula, just to make sure that all of the dry ingredients are completely blended into the dough.
Use a rounded teaspoon of dough for each cookie take the spoonful of dough from the bowl and then shape it into a ball between your palms. Place the balls about 2 inches apart on the baking sheets. Using the end of a wooden spoon or your knuckle, press a thumbprint into the center of each ball of dough.
Bake the cookies for 9 to 10 minutes, or until they are dry and feel firm to the touch. If your oven has hot spots, rotate the baking sheets top to bottom and front to back after 4 minutes in the oven. Leave the cookies on the baking sheets while you work on the filling.
Place white baking pieces in a microwave safe bowl. Microwave on 100% power (high) for 45 to 60 seconds; stir until melted and smooth. Use a small spoon to fill each thumbprint with chocolate. Alternatively and more neatly you can fill a small zipper-lock bag with the chocolate, press out the air, seal it and then cut off a tiny triangle of the bag at one of its corners. Squeeze a little chocolate into each cookie. Top with red sprinkles.
If you'd like, refrigerate the cookies for 15 minutes to set the chocolate. Serve at room temperature.