Make the cake: Preheat oven to 350°F (180°C). Spray two 8" (or three 6") round cake pans with baking spray and parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter and sugar at medium speed until fluffy, 3 to 4 minutes. Add egg whites, one at a time, beating well after each addition. Beat in vanilla.
In a food processor (or blender), pulse freeze-dried strawberries until powdered, 5 to 6 times.
In a medium bowl, whisk together flours, baking powder, salt, and strawberry powder. Gradually add flour mixture to butter mixture alternately with milk, beginning and ending with flour mixture, beating just until combined after each addition.
Bake until a wooden pick inserted in center comes out clean, 25 to 30 minutes.