Preheat the oven to 350F degrees F. Place cupcake papers in a cupcake pan.
In a stand mixer, cream the 9 Tablespoons softened butter and 3/4 cups sugar until combined fluffy.
Place the white chocolate in the microwave for 20 second intervals until completely melted. Make sure not to burn. Add the white chocolate to the sugar /butter mixture.
Start adding the dry ingredients (baking powder, baking soda and all-purpose flour).
You will alternate the dry ingredients with the milk. A little flour then a little milk and continue until its all been incorporated.
Finally mix in the vanilla extract. Mix until combined. Be careful to not over-mix.
In another bowl, whisk the egg whites until they are light and fluffy. Add in the leftover 1 ½ tablespoons of sugar, little by little.
Once the egg whites form peaks, fold them into the cupcake mixture.
Distribute the batter evenly into cupcake liners, filling each liner about ⅔ of the way up.
Bake for 19-20 minutes at 350F degrees or until you insert a toothpick and it comes out clean. Allow cupcakes to cool completely before starting on the frosting.
To make the buttercream, using a stand mixer or an electric hand mixer, cream the butter until light and fluffy.
Add in the sifted powdered sugar, little by little, alternating with the vanilla extract and heavy whipping cream.
Mix until fluffy and transfer into three separate bowls.
Add in the food coloring to each of the bowls and mix until the color is even throughout all the buttercream (note: one bowl will not have added color. It will be the white part of the frosting swirl).
Transfer each color into its own a piping bag.
Take a piece of plastic wrap and lay it on then counter. Then take the blue color piping bag and spread a line over the plastic wrap. The line should measure approximately the length of your piping bag. It should fit into the bag and fill it almost completely in length. Repeat once again on top so you have a line that is double the thickness.
Continue doing the same thing for the red color, then the white, and repeat each color once more until there are two blue lines, two white, and two red.
Roll one edge in until it touches the last color which should be white. At the end, the blue touches the white color. This will give you the shape of a cylinder. Tie up the edges.
Cut one of the edges and place that part into the bottom of another piping bag sleeve with your decorating tip placed. This way your dollop of icing will be three colors and the colors won't smudge together.
Add a large swirl onto each cupcake, from the outside inwards. Then serve!