Step 1: Preheat your oven to 325°F (160°C). Line a 9x13-inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
Step 2: In a medium bowl, combine gluten-free graham cracker crumbs, 1/4 cup granulated sugar, and melted butter. Mix until evenly moistened.
Step 3: Press the crumb mixture firmly and evenly into the bottom of the prepared baking pan. Bake for 10 minutes. Remove from oven and let cool slightly while you prepare the filling.
Step 4: In a large bowl, using an electric mixer, beat the softened cream cheese and 1 cup granulated sugar on medium speed until smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl as needed.
Step 5: Beat in the eggs one at a time, mixing just until each is incorporated. Do not overmix. Stir in the vanilla extract, peppermint extract, and salt.
Step 6: Gently fold in the sour cream (or Greek yogurt) and 1/2 cup of crushed candy canes until just combined.
Step 7: Pour the cheesecake filling over the cooled crust and spread evenly. Bake for 35-40 minutes, or until the edges are set but the center still jiggles slightly when gently shaken.
Step 8: Turn off the oven, crack the door open slightly, and let the cheesecake cool in the oven for 30 minutes. This helps prevent cracking.
Step 9: Remove the pan from the oven and let it cool completely on a wire rack at room temperature. Once cool, cover and refrigerate for at least 4 hours, or preferably overnight, until thoroughly chilled and set.
Step 10: Once chilled, use the parchment paper overhang to lift the cheesecake out of the pan. Cut into 16 bars. Garnish with additional crushed candy canes before serving.