Step 1: Prepare Your Baking Dish - Line your 9x9-inch baking dish with parchment paper, allowing some overhang for easy removal later.
Step 2: Melt the Chocolate Mixture - In a medium saucepan over low heat, combine the sweetened condensed milk, chopped semi-sweet chocolate, and butter. Stir continuously until the chocolate and butter are completely melted and the mixture is smooth.
Step 3: Add Flavorings - Remove the saucepan from heat and stir in the peppermint extract and vanilla extract until well combined.
Step 4: Fold in the Candy Canes - Gently fold in the crushed candy canes, reserving a tablespoon for topping if desired.
Step 5: Pour and Set - Pour the fudge mixture into the prepared baking dish, spreading it evenly. Sprinkle reserved candy canes on top if using. Allow to cool at room temperature before refrigerating for about 2-3 hours.
Step 6: Cut and Enjoy - Once the fudge is firm, lift it out using the parchment paper overhang, place on a cutting board, and slice into squares.