Preheat oven to 325°. Line cupcake pans with paper liners; set aside. In the bowl of an electric mixer fitted with the paddle attachment, combine flours, sugar, baking powder, and salt; mix on low speed until combined. Add butter, mixing until just coated with flour.
In a large glass measuring cup, whisk together eggs, milk, and vanilla. With mixer on medium speed, add wet ingredients in 3 parts, scraping down sides of bowl before each addition; beat until ingredients are incorporated but do not overbeat.
Divide batter evenly among liners, filling about two-thirds full.
Bake, rotating pan halfway through, until a cake tester inserted in the center comes out clean, 17 to 20 minutes.
Transfer to a wire rack to cool completely. Repeat process with remaining batter.