Preheat the oven to 325 degrees F. Butter six 6-ounce ramekins or ten 4-ounce ramekins. Place the ramekins all in a large rimmed baking dish.
Whisk the egg yolks with the sugar, vanilla, peppermint extract and salt. Then pour the cream into a separate microwave-safe bowl and microwave until it simmers. Whisk the egg mixture FEVERISHLY, and slowly pour the hot cream into the egg. POUR SLOWLY to ensure you don't scramble your eggs. Then evenly distribute the finished mixture among the prepared ramekins.
Carefully pour hot water around the ramekins in the baking dish about half way up the sides, then place in the oven.
Bake for 35-45 minutes—closer to 35 for smaller ramekins and 40-45 minutes for larger ramekins. The edges should be firm and the very center should jiggle just a little. Remove from the oven and cool until easy to handle. Then cover the tops with plastic wrap and chill for at least 4 hours, but up to a week.
One hour before serving, crush the candy canes in a food processor or blender, and sprinkle the candy cane powder over the top of each custard.
Using a brulee torch, caramelize the top of each custard, then place them back in the fridge for at least twenty minutes to harden. *If you don't have a brulee torch, you can place the whole tray of ramekins under the broiler to brulee the top. Make sure it is fiery hot when you put them in, and DON'T TAKE YOUR EYES OFF THEM FOR A SECOND. If the broiler is hot enough, this should take less than a minute.