Preheat oven to 350 degrees F. Place liners in a standard size muffin pan and set aside.
Place white chocolate chips in a microwave safe bowl and drizzle with vegetable oil. Microwave, 15 seconds at a time, stirring after each microwaved time, until chocolate is 90% melted. Stir to melt the rest of the chocolate, until smooth, and set aside to cool.
Add butter and sugar to the bottom of a stand mixer and beat on MED HIGH speed until fluffy and light in color, about 2-3 minutes.
Add in eggs, one at a time, scraping down the sides of the bowl as needed.
Beat in the cooled white chocolate and vanilla extract.
To a medium mixing bowl, add both flours, baking powder and salt. Whisk to combine.
Add in flour, one third of the mixture at a time, and alternating with the buttermilk, on LOW speed until just combined. Scraping the sides of the bowl as needed.
Using a large cookie scoop or one third measuring cup, scoop the batter into the paper liners, filling them about 2/3 (two thirds) of the way full.
Bake approximately 25-30 minutes, until a toothpick inserted into the center of a cupcake comes out clean.
Cool in muffin tin for 2 minutes, then remove to a cooling rack to cool completely.
FOR THE FROSTING:
Add butter to the bowl of a stand mixer and beat on MED HIGH for about 4-5 minutes, until very light and fluffy.
Add in powdered sugar and beat on LOW until combined.
Mixture will look very dry.
Add heavy cream and peppermint extract and beat on LOW until smooth and silky.
Add food coloring, if using.
Turn mixer speed up to MED or MED HIGH and beat for several minutes, until light and airy.
Spoon into pastry bag fitted with a decorating tip (I used an open star tip) and pipe onto cooled cupcakes.
Sprinkle with crushed candy canes or sprinkles.