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 small cookie scoop or spoon, scoop the batter into the paper liners, filling them about 2/3 (two thirds) of the way full.
Bake approximately 12-15 minutes, or 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.
Make sure cupcakes are completely cooled before frosting.
In a stand mixer (or with hand mixer), cream butter until it is light and fluffy.
Add salt and 1/2 of powdered sugar. Beat on low speed until sugar is slightly incorporated, then add remaining 1/2 of the powdered sugar. Frosting will look dry at this point.
Add champagne and heavy cream and beat another 2-3 minutes.
Add frosting to a piping bag fitted with a star tip (or whichever you prefer) and frost cupcakes as desired.