Line two half-sheet pans with parchment paper and set aside.
Add the chocolate chips and 2 teaspoons of oil to a medium-sized microwave-safe glass bowl. Microwave for 60 seconds, then stir. Continue microwaving in 20-second increments, stirring after each, until melted and smooth.
Dip the mini pretzels into the melted chocolate, allowing the excess to drip off, then place them on the prepared sheet pans. Immediately sprinkle crushed candy canes over the melted chocolate. If the chocolate in the bowl gets too thick, microwave it for 15 seconds, then stir until smooth.
Add the white chocolate chips and the remaining 1 teaspoon of oil to a small microwave-safe glass bowl.
Microwave for 45 seconds. Stir, then microwave in 20-second increments, stirring after each, until the white chocolate is melted and smooth.
Use a spoon or fork to drizzle the white chocolate over the pretzels, or transfer the melted white chocolate to a zip-top plastic bag. Seal the bag, snip off a small corner, and drizzle it over the pretzels.
Let the chocolate peppermint-dipped pretzels sit at room temperature until the chocolate has set, about 30 to 40 minutes, before serving.