1.Preheat oven to 350 degrees. Line a 12-cup muffin tin with cupcake liners; set aside.
2.Place strawberries in a small food processor; process until pureed. You should have about 1/3 cup of puree, add a few more strawberries if necessary or save any extra puree for frosting; set aside.
3.In a medium bowl, whisk together flour, baking powder, and salt; set aside. In a small bowl, mix together milk, vanilla, and strawberry puree; set aside.
4.In the bowl of an electric mixer fitted with the paddle attachment, cream butter on medium-high speed, until light and fluffy. Gradually add sugar and continue to beat until well combined and fluffy. Reduce the mixer speed to medium and slowly add egg and egg whites until just blended.
5.With the mixer on low, slowly add half the flour mixture; mix until just blended. Add the milk mixture; mix until just blended. Slowly add remaining flour mixture, scraping down sides of the bowl with a spatula, as necessary, until just blended.
6.Divide batter evenly among prepared muffin cups. Transfer muffin tin to oven and bake until tops are just dry to the touch, 22 to 25 minutes. Transfer muffin tin to a wire rack and let cupcakes cool completely in tin before icing.
Place strawberries in the bowl of a small food processor; process until pureed. In the bowl of an electric mixer fitted with the paddle attachment, beat together butter and salt on medium speed until light and fluffy. Reduce mixer speed and slowly add confectioners' sugar; beat until well combined. Add vanilla and 3 tablespoons strawberry puree (save any remaining strawberry puree for another use); mix until just blended. Do not overmix or frosting will incorporate too much air. Frosting consistency should be dense and creamy, like ice cream.