1. Position an oven rack in the center position and preheat the oven to 350°F
2. Place the white chocolate in a heatproof bowl. Bring a skillet of water to a simmer over medium heat. Turn off the heat and place the bowl in the hot water. Let it stand, stirring occasionally, until the chocolate is completely melted and smooth. Be careful not to let any water get in the bowl or the chocolate will seize and clump. Remove the bowl from the water and let cool.
3. In a small bowl, whisk together the all-purpose flour, cake flour, baking powder, and salt.
4. In a glass measuring cup, stir together the milk and vanilla.
5. In the bowl of a stand mixer or in a large bowl with a handheld electric mixer, beat the sugar and butter on high speed until light and fluffy, about 3 minutes. Beat in the eggs, 1 at a time, scraping the sides of the bowl as needed. Beat in the tepid chocolate. Reduce the speed to low and beat in the flour mixture in 3 additions, alternating with the milk mixture in 2 additions, and mix until smooth. Using a 2-inch diameter ice cream scoop or a 1/3 cup measuring cup, scoop the batter into the prepared cups. The cups should not be more than 2/3 full. (If you overfill the cups, they will end up flat rather than domed.)
6. Bake until a wooden toothpick inserted in the center of a cupcake comes out clean, 25 to 30 minutes. Do not over bake. Don’t be alarmed if the cupcakes don’t rise appreciably or if they fail to turn golden brown. Let the cupcakes cool for 10 to 15 minutes. and
7. Frost the tops of the cupcakes with the frosting.