Step 1: Line an 8×8 inch baking pan with parchment paper, leaving a generous overhang on the sides to easily lift the fudge out later. Lightly grease the parchment paper itself with butter or a neutral non-stick cooking spray.
Step 2: In a large, heavy-bottomed saucepan, combine the chocolate chips, sweetened condensed milk, and butter pieces. Place over medium-low heat.
Step 3: Stir constantly with a heat-resistant spatula until the chocolate is completely melted and the mixture is smooth, homogenous, and glossy. This should take about 3-5 minutes. Do not scorch the chocolate.
Step 4: Remove the saucepan from the heat immediately. Stir in the vanilla extract and peppermint extract. Mix thoroughly until fully incorporated.
Step 5: Pour the hot fudge mixture into the prepared baking pan. Spread evenly with the spatula. Immediately sprinkle the crushed candy canes generously over the top of the hot fudge, gently pressing them into the surface.
Step 6: Place the pan, uncovered, in the refrigerator for at least 2-3 hours, or until the fudge is completely set and firm. For faster setting, you can place it in the freezer for about 30-45 minutes.
Step 7: Once set, use the parchment paper overhang to lift the fudge from the pan onto a clean cutting board. Warm a sharp knife under hot water, wipe it dry, and cut into 1-inch squares. Re-warm and wipe between cuts if needed.
Step 8: Store any leftover fudge in an airtight container at room temperature for up to 1 week, or in the refrigerator for up to 2 weeks. It also freezes well for up to 3 months; thaw at room temperature before serving.