Line an 8 × 8-inch metal or ceramic baking dish with parchment paper, allowing the paper to overhang the sides for easy removal. Fold the corners to fit snugly against the pan and spray the parchment lightly with cooking spray.

In a small saucepan, combine the heavy cream and butter. Warm over medium heat until the mixture is steaming. Remove from the heat, then stir in the peppermint extract, vanilla extract, and salt. Cover and set aside to keep warm.

In a large, high-sided saucepan, combine the granulated sugar, corn syrup, and water. Stir gently until blended. Using a clean pastry brush dipped in water, wash down any sugar crystals clinging to the inside of the pan. Attach a candy thermometer to the side of the saucepan, ensuring the tip is submerged in the syrup but not touching the bottom.

Cook the mixture over high heat without stirring until it reaches 270 °F (132 °C), about 15 minutes. If sugar crystals form along the sides, brush them away carefully with the wet pastry brush, avoiding excess water.

When the sugar mixture reaches 270 °F, carefully add the warm cream and butter mixture a little at a time, stirring gently after each addition. Stand back from the pot to avoid steam burns. Continue cooking over medium-high heat, without stirring, until the caramel reaches 245 °F to 250 °F (118 °C to 121 °C) and turns a deep golden color. Tilt and swirl the pan occasionally to ensure even cooking.

Remove the saucepan from heat and immediately pour the hot caramel into the prepared pan. Do not scrape the bottom of the pot, as any crystallized sugar may alter the texture. Let the caramel cool for 10 minutes, then cover the pan loosely with plastic wrap and refrigerate until firm, about 1 hour.

Once chilled, lift the caramel slab from the pan using the parchment overhang. Transfer to a cutting board and cut into 1-inch strips, then into 1-inch squares. If desired, lightly roll each piece in finely crushed candy cane powder. Wrap each caramel individually in 1 ½ × 3-inch pieces of parchment or wax paper, twisting the ends to seal.

Store wrapped caramels at room temperature in an airtight container for up to 3 weeks. For longer storage, refrigerate or freeze in layers separated by wax paper.