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Combine 3/4 cup of sugar, 1 1⁄2 tablespoons (22.2 ml) of all purpose flour, and 1/2 cup of unsweetened cocoa powder in a bowl. Mix them together with a fork or whisk to combine them evenly and remove any lumps there might have been. Bring a saucepan up to medium heat, then add 1 1/4 cups of milk, 2 tablespoons (29.6 ml) of unsalted butter, and 1⁄2 tablespoon (7.4 ml) of vanilla extract. Stir the ingredients until the butter has melted completely. Add more vanilla extract for stronger flavor, but don’t go overboard! If you try to dump all the dry ingredients into the saucepan at once, you’ll have a flour-bomb. Instead, add the dry ingredients little by little, whisking them into the wet ingredients to even out any lumps. Keep stirring the sauce to keep it from burning over the higher heat. After about five to six minutes, turn off the heat completely and add a pinch of salt to add depth to the flavor. There are many ways you can do this, so use whatever is handy in your kitchen.  The most obvious method would be to use a mortar and pestle. Snap the candy into smaller, more manageable pieces, and put them in the mortar a few at a time. Use the pestles to grind the candy down into a powder or small shards — whichever you prefer. You can also use a hammer or meat tenderizer. Place the candy cane in a sealable plastic bag, snapping it into smaller pieces to fit if needed. Place the bag on a stable surfaces, then pound at the candy with the hammer or meat tenderizer until it reaches the texture you prefer. Use whatever you can find around the house. Be creative, but be safe. Use a vegetable peeler to remove the outer skin from the apple, being careful not to cut your fingers in the process. Stand the apples up, then, using a sharp knife, slice down along the edges of the core to remove the edible flesh of the apple from the inedible core. Cut the edible flesh into smaller slices as you see fit. Lay them out either on a large plate or over a length of tin foil, if you want to avoid the extra dishes. You can finish your chocolate apples any way you like. Some choices might include:  Dip the entire apple slice in chocolate sauce, or dip only half the slice. Use a spoon to drizzle chocolate sauce lightly over the apple slices. Wag a spoonful of sauce quickly back and forth, allowing the chocolate to drizzle down lightly over the apple slices. Top them with the crushed candy, letting the sauce work as an adhesive. Put out a bowl of chocolate sauce and a bowl of crushed peppermint, allowing your guests to dip and sprinkle themselves, deciding how much garnish they want for their apples. Refrigerating them before serving them sets the chocolate a little bit, which some people prefer.

Summary:
Mix the dry ingredients for the chocolate sauce. Combine wet ingredients for chocolate sauce over heat. Add the dry ingredients a small portion at a time. Increase heat to medium-high and simmer. Crush the candy canes into powder. Peel and core your apples. Top the apple slices with chocolate sauce and crushed candy cane.