Special equipment: a 12-count muffin tin, cupcake liners
Preheat the oven to 350 degrees F.
For the batter: In a stand mixer fitted with a paddle attachment, combine the butter and sugar and beat until light and fluffy. One at a time, add the eggs, mixing each one in completely before adding the next. Add the vanilla and beat to combine.
In another bowl, sift or whisk together the flour, baking powder and salt. With the mixer running, add a third of the flour mixture and then the milk, beating just to incorporate. Beat in the remaining flour mixture. Divide the batter between two bowls and set one bowl aside (this will be the white cake batter).
Mix the cocoa powder into the remaining bowl of batter (this will be the chocolate batter).
Line a muffin tin with cupcake liners or spray with nonstick cooking spray. Divide the white cake batter evenly among the muffin cups, and then do the same with the chocolate batter.
Bake until a cake tester comes out clean, 15 to 18 minutes. Cool slightly, then transfer to a wire rack to cool while you prepare the buttercream.
For the strawberry buttercream: Puree the strawberries in a blender until completely smooth. Press through a fine-mesh sieve into a small saucepot. Bring to a boil over medium-high heat and cook, stirring frequently, until reduced by half, about 10 minutes; you'll need at least 1/2 cup. Cool completely.
In a mixing bowl, add 3 cups of the confectioners' sugar, the butter and the vanilla and beat with a hand mixer until combined. Add the strawberry reduction, beat until incorporated, and then gradually add the remaining 1 cup confectioners' sugar. Transfer to a piping bag fitted with a round tip and pipe the buttercream onto the cupcakes.