Set oven rack in middle position and preheat oven to 350 degrees. Line two 12-cup muffin tins with cupcake liners or spray with cooking spray, and set aside.
Place your freeze-dried strawberries in a food processor and grind them to a powder*. Set aside for later use.
Pour milk, egg whites, and vanilla into 2-cup measuring cup, and mix with fork until blended.
Mix cake flour, sugar, baking powder, and salt in bowl of electric mixer on low speed. Add butter and continue mixing on low speed until mixture resembles moist crumbs, with no powdery streaks remaining.
Add all but 1/2 cup of milk mixture to crumbs and beat at medium speed for 1½ minutes. Add remaining 1/2 cup of milk mixture and mix an additional 30 seconds, scrape down the sides and then mix 20 seconds more.
Mix in strawberry powder until just blended, then stir in minced basil.
Divide batter evenly into prepared cups. Bake until toothpick inserted in the center comes out clean, 15-17 minutes (8-11 for miniature).
Cool completely before frosting.