Pour brewed coffee and 1/4 cup milk in to a small saucepan and cook over low heat.
Add sugar, cocoa, and chocolate to saucepan and cook until chocolate has melted completely. Use a whisk to break up any chocolate clumps at the bottom.
Add peppermint extract and stir in.
Divide among two coffee cups.
To make the milk froth, add remaining 1/4 cup of milk to a mason jar or microwave safe jar with a lid. Tighten lid and shake milk vigorously for one minute. Remove lid and microwave for 30 seconds.
Holding back froth, pour warm milk evenly among the two cups.
Spoon froth onto mocha lattés and top with crushed candy cane pieces.