In a microwave safe bowl, microwave half the milk chocolate and the vegetable oil on 50% power for 2 minutes. The vegetable oil keeps the chocolate from setting to quickly.
You will want to stir after 30 seconds to a minute and check every 30 seconds after that until the chocolate is melted.
Once the chocolate starts to melt, add the rest of the chocolate and microwave again for 2 minutes on 50% power.
You may need to do this 4 times to melt all the chocolate.
Remove from the microwave once it is melted and stir. Add the peppermint oil and stir again to incorporate.
Pour the chocolate onto a silicone mat that is on a cookie sheet. Use a spatula to spread the chocolate over the mat and allow to cool.
Slight drop the baking sheet onto the counter to help settle the chocolate.
While the chocolate is setting, start melting the white chocolate and repeat the process for melting the chocolate. You do not need to add peppermint oil to the white chocolate (unless desired) or the vegetable oil.
Once melted, stir and the pour on top of the milk chocolate and spread evenly.
Gently. Gently, bang the tray on the counter to 'tunk' it to even it out.
Take the crumbled peppermint candy and sprinkle on top of the white chocolate.
Press the peppermint candy into the chocolate to keep it in place.
Allow the chocolate to set before breaking into small pieces.
Place in jars, bags or your favorite holiday container for gifts.