Make the crust: In the bowl of a food processor fitted with the blade attachment, combine flour, sugar and salt. Pulse in chilled butter until mixture forms into pea-like clumps. Drizzle in chilled water. Remove dough from bowl, form into a disc and wrap in plastic wrap. Refrigerate for 30 minutes.
Preheat oven to 375. Roll into a large circle, approximately 12 by 18 inches and form into a pie plate. Refrigerate for 30 minutes and fill the bottom of the pie plate with beads or beans to prevent from tenting. Bake for 20 to 25 minutes until golden. Set aside to cool for up to 2 hours.
Make the filling: In a small bowl, mix clear gelatin and 3 tablespoons of sugar. Hydrate gelatin with 1/2 cup water and set aside. Mixture will look like applesauce. In a medium saucepan, heat 2 cups water and 2 cups of sugar to a near boil, approximately to 180 degrees. Add gelatin mixture once set until dissolved. Remove from heat and add remaining cold water, citric acid and peppermint extract. Pour into set crust and refrigerate for 6 hours or up to overnight.
Serve pie with whipped cream and crushed candy canes. Pie will keep up to 4 days refrigerated.