Grease an 8 x 8-inch square pan and line with parchment paper, leaving an inch overhang.

Combine 1 can sweetened condensed milk, 3/4 cup evaporated milk, 3 tablespoons butter, cocoa powder, instant coffee, vanilla extract, and a pinch of salt in a large saucepan.

Place over medium heat and bring to a boil. Cook, stirring constantly with a wooden spoon, until mixture has thickened, reduced by 2/3 to 3/4, and when you drag your spoon along the bottom the mixture stays separated for 5-6 seconds before running back together, about 20-30 minutes. If mixture is bubbling too vigorously, turn down the heat as you stir to maintain a slow boil.

Pour into pan and smooth into an even layer. Let stand 30 minutes. Clean saucepan and spoon.

Combine remaining condensed milk, evaporated milk, butter, peppermint extract, and pinch of salt in the clean saucepan and repeat the cooking process with the peppermint mixture.

Once mixture is cooked and thickened, reserve 2 tablespoons of the crushed candy canes then stir the rest into the peppermint mixture. Pour over chocolate mixture and smooth the top. Sprinkle reserved crushed candy canes on top and let sit at least 1 hour before cutting.