Preheat oven to 200 degrees F.
Place sugar, water, and corn syrup into a saucepan and bring to a boil. This is when to add the candy thermometer. Without stirring allow it to reach the "soft crack stage" (285°F). Remove from heat. When the bubbles subside, stir in the peppermint extract.
Divide the candy into two parts, pouring out half of the candy onto a baking sheet that's been sprayed with non-stick cooking spray. To the remaining part left in the saucepan, add a few drops red food coloring. Mix and pour onto another baking sheet sprayed with non-stick cooking spray. Place it in a 200 degree F oven to keep it warm.
When a skin forms on the red candy, use a metal spatula to knead and fold the candy over itself. Do this for 2-3 minutes until the mixture is cool enough to handle.
Using heat-resistant gloves, pull the red candy into a long rope, fold it in half, doing this a few times until it starts becoming difficult to work with. Finally, twist it together until it's about a 2-inch-wide rope. Place it back on the baking sheet and into the warm oven while you work on the other half of the candy (which you'll add white food coloring to) and repeat the process, creating a white rope.
Cut a 3" section of each rope and press them together. Then pull and twist together, and bend a shepherd's crook—these are your candy canes! Let them fully harden. Store in an airtight container.
